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Publications 

OF THE 

American Economic Association 
Vol. XI. No. 4. Pages 331-442. 

Appreciation and Interest 



A STUDY OF THE INFIvUENCE OF MONETARY APPRECIA- 
TION AND depreciation ON THE RATE OF INTER- 
EST, WITH APPLICATIONS TO THE BIMETALLIC 
CONTROVERSY AND THE THEORY OF INTEREST. 

BY 

IRVING FISHER, 

Assistant Professor of Political Science in Yale University. 



AUGUST, 1896. 



PUBLISHED FOR THE 

American Economic Association 

BY The Macmii,lan Company 

NEW YORK 

LONDON : SWAN SONNENSCHEIN & CO. 



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^ta--,.*/api^ 



Q- 






537 



Copyright 1896 by 
American Economic Association 



PRESS OF 

Andrus & Church, 
ithaca, n. y. 



^ 






APPRECIATION 

AND 

INTEREST. 



Digitized by the Internet Arciiive 
in 2010 with funding from 
The Library of Congress 



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CONTENTS. 



Part I. Thkory. 

PAGE. 

Chapter I. Introduction. 

li. Does appreciation necessarily aggravate debts? . ... i 

§2. Efforts to find a "just" standard i 

I 3. Invariability of standard not essential 3 

I 4. Bearing of the rate of interest on the subject .... 3 

Chapter II. One year contracts. 

I I. Foreseen and unforeseen appreciation or depreciation, 6 

I 2. One year contract, numerical illustration 6 

I 3. Formula connecting interest and appreciation .... 8 

§4. Money as standard and as medium 11 

Chapter III. More than one year. 

I I. Confusion in separating interest and principal .... 12 

I 2. Compound interest, five years 12 

? 3. General formula I3 

I 4. Partial payments, seven years i4 

I 5. General formula 16 

I 6. Special case • ^^ 

Chapter IV. Present value. 

I I. Different modes of payment do not aflfect present value, 19 
I 2. Illustration when interest is paid annually and princi- 
pal redeemed at maturity 20 

I 3. Case of perpetual annuity 21 

^ 4. Formula ^^ 

Chapter V. Varying rates of appreciation. 

I I. Numerical illustration 23 

§ 2. Average rate of interest 24 

? 3. Formula for varying rate of interest 26 

^ 4. Formula for average rate of interest 26 

I 5. Formula for average rate of appreciation 28 

I 6. Practical application 28 

Chapter VI. Zero and negative interest. 

I I. Limits to rates of interest and appreciation 3° 

I 2. Effect of hoarding 3^ 

I 3. Negative interest possible 32 

I 4. Investment not necessarily checked by zero interest . 33 



vi Contents [338 
Part II. Facts. 

Chapter VII. Introduction. 

§ I. Objections 35 

§ 2. Existence of foresight in general 36 

Chapter VIII. Gotd atid paper. 

§ I. General evidence 38 

^ 2. United States currency and coin bonds 39 

f 3. Extent of foresight in gold premium 41 

? 4. Dangers of preceding method 44 

Chapter IX. Gotd and stiver. 

? I. India "rupee paper" and gold bonds 46 

I 2. Extent of foresight in Indian exchange 49 

§3. Upper limit of gold borrower's loss in England . . . 51 

^ 4. Bearing of a rupee debt on Indian finance 52 

Chapter X. Money and commodities. 

§ I. Difficulties in comparing successive periods 54 

I 2. Rate of interest as related to high and low prices . 54 
§ 3. Rate of interest as related to rising and falling prices 

in England 56 

§ 4. Rate of interest as related to rising and falling prices 

in Germany, France, and the United States .... 60 
§ 5. Rate of interest as related to rising and falling prices 

in silver standard countries 63 

^ 6. Measurement of foresight for short periods 66 

I 7. Error of Jevons, Price, and others 67 

^ S. Measurement of foresight for long periods, in England 70 

I 9. Lower limit of borrower's loss in England 71 

§ 10. Loss on contracts made before 1873, ^'^ England ... 73 

§11. Measurement of foresight for long periods, in America, 74 
§ 12. Theory as to mode of adjusting rate of interest to 

price movements 75 

I 13. Credit cycles 76 

Part III. Applications. 

Chapter XI. The bimetallic controversy. 

§1. Magnitude of debtor's loss 80 

§ 2. Index numbers 81 

? 3. Bimetallism could not correct losses 82 

§ 4. Bimetallism would violate contracts 83 

§ 5. Fallacy that we can predict further losses 85 

^ 6. Bimetallism to secure stability in standard 86 

Chapter XII. The theory of interest. 

\i. "Real" and "nominal" interest, inadequate terms, 88 



339] Contents. 



vn 



I 2. An absolute standard is individualistic 90 

I 3. Interest varies with length of contract 91 

§ 4. Multiple theory of interest 91 



Appe;ndix. StatisticaIv Data. 

§ I. Table of interest rates each year in seven countries . . 93 

I 2. References to other statistics of the rate of interest . . 96 

I 3. Index numbers of prices and wages 98 



STATISTICAI. TABLES. 

Rates of interest realized on United States "coin" and " cur- 
rency " bonds from dates mentioned to maturity 39 

Rates of interest realized on United States "coin" and "cur- 
rency " bonds from dates mentioned to January i, 1879, 

(date of Resumption) 42 

Rates of interest realized on India gold and silver bonds from 

dates named to maturity or in perpetuity 47 

Rates of interest realized on India gold and silver bonds for 

periods specified 5^ 

Market rates of interest in seven countries, in relation to high 

and low prices ... 55 

London rates of interest in relation to rising and falling prices, 59 
Berlin rates of interest in relation to rising and falling prices . 61 

Paris rates of interest in relation to rising and falling prices . 61 

New York rates of interest in relation to rising and falling prices 

and wages "^ 

Average bank rates in gold and silver standard countries before 

and after the breakdown of bimetallism 64 

Rates of interest in relation to rising and falling prices in Cal- 
cutta, Tokyo and Shanghai 65 

Number of cases in seven countries favorable and unfavorable 
to the theory that rising and falling prices are associated 

respectively with high and low interest 66 

London market rates of interest in relation to rising and falling 

prices, wages and incomes for long periods 7° 

New York rates of interest in relation to rising and falling 

prices and wages for long periods 74 

Yearly average rates of interest on "money" in seven coun- 
tries 94 

Index numbers for seven countries 99 



PREFACE. 



The connection between monetary appreciation and the 
rate of interest has received very scant attention from econ- 
omists. The writer has been led to beUeve that this neglect 
has somewhat retarded the progress of economic science and 
the successful interpretation of economic history — in particu- 
lar the monetary history of the last twenty years. The views 
here put forward were first stated in brief before the Ameri- 
can Economic Association at Indianapolis, December, 1895. 
They differ radically from those expressed by Mr. Giffen and 
many other eminent economists. For this reason it has been 
necessary to make a statistical examination of all available facts 
bearing on the subject. Such a study could not be properly 
conducted without a definite economic theory as a starting 
point. The idea on which this theory is founded appears to 
have occurred independently to several writers, of whom Mr. 
Jacob de Haas, Jr., of Amsterdam, seems most fully to have 
realized its importance. To develop the theory in a quanti- 
tative form, some simple mathematics have been employed. 
With numerical illustrations at each step, it is hoped 
that those to whom mathematics are distasteful will find few, 
if any, impediments to easy reading. The mathematical 
reader, on the other hand, may feel that the discussions are 
too much encumbered by numerical illustration and detail ; 
but these presentations are usually in such a form that they 
can easily be passed over by those who find them superfluous. 
The gist of the theory is contained in Chapter II, but its 
statement would not be complete, nor the apparent objections 
to it fully answered, without the discussions of Chapters 
III-VI. 



X Preface. [342 

The writer is greatly indebted to the many persons whose 
names are mentioned in the text, who have supplied him 
with important facts and references ; also to Professor Sum- 
ner for the privilege of consulting his collection of works on 
banking ; to Professor Hadley, for valuable suggestions and 
criticisms ; to Mr. Horace White for pointing out the im- 
portant pamphlet of the eighteenth century mentioned in 
Chapter I ; and to Mr. Sakata for translating several statis- 
tical tables from Japanese. 

New Haven, August, 1896. 



PART I. THEORY. 
CHAPTER I. 

INTRODUCTION. 

§1. 

The chief issues in the bimetallic controversy center 
about the question of justice between debtor and creditor. 
The bimetallic propaganda succeeds just so far as it 
spreads a belief that an injustice has been done by the 
adoption of the gold standard, which the re-adoption of 
bimetallism would correct. 

The question therefore arises, does the appreciation of 
gold necessarily aggravate debts? Are contracting 
parties powerless to forestall the gains or losses of an 
upward or downward moving currency ? It is clear that 
if the unit of length were changed and its change were 
foreknown, contracts would be modified accordingly. 
Suppose a yard were defined (as once it probably was) to 
be the length of the king's girdle, and suppose the king 
to be a child. Everybody would then know that the 
"yard" would increase with age and a merchant who 
should agree to deliver i,ooo " yards " ten years hence, 
would make his terms correspond to his expectations. 
To alter the mode of measurement does not alter the 
actual quantities involved but merely the numbers by 
which they are represented. 

§2. 

Hitherto monometallists have usually replied to the 
argument "gold has appreciated, therefore the debtor 



2 American Economic Association. [344 

has been robbed " by challenging, not the inference, but 
the premise. Thus the discussion has been shunted off 
from economic theory and turned into a controversy 
over the fact of "appreciation." This controversy has 
been, to a large extent, a mere war of words, because, by 
" appreciation " the monometallists mean one thing and 
the bimetallists, another. No one has ^-et provided a 
meaning for that much abused word acceptable to both 
parties. The bimetallists prove the appreciation of gold 
by the fall in prices. The monometallists reply that 
wages have risen, and hold that the fall in prices is due 
to progress in the arts. Some bimetallists, e. g.^ Leonard 
Courtney,^ accept the distinction between a fall in prices 
through causes connected with gold and a fall through 
causes connected with commodities, but most of them 
assert that a " fall of prices " and " appreciation of gold " 
are synonymous expressions, and that, if progress cheap- 
ens other commodities, it ought justly to cheapen gold 
also. Generally speaking, bimetallists set up the " com- 
modity standard " and monometallists, the " labor 
standard." 

Others attempt to find the "just" standard in "mar- 
ginal utility," " total utility," and so forth. On all sides 
it is tacitly assumed that a "just" standard must in 
some sense be an " invariable " standard ; that is, a 
standard such that the principal of the debt when due 
should be equivalent in some way to the original loan. 
" All writers on the subject of money have agreed that 
uniformity in the value of the circulating medium is an 
object greatly to be desired — a currency to be perfect, 
should be absolutely invariable in value." " Proposals 

1 Report of the Indian Currency Committee, 1S93, p. 39; also, 
Nineteenth Century, April, 1893. 

^ Ricardo, "Proposals for an Economic and Secure Curreuc}'," 
Sees. I, II. 



345] Appreciation and Interest. 3 

to define and secure such invariability have been made 
by many writers. Within the last few years, the prob- 
lem has become a favorite one and scarcely an issue of 
the economic journals appears without discussions on 
" The ultimate standard of value," " The just standard 
of deferred payments," " Has gold appreciated ? " " The 
measurement of the value of money," and kindred sub- 
jects.^ 

§3. 
It is not prosposed to deny that the terms appreciation 
and depreciation may have an " absolute " as distinct 
from a " relative " meaning.^ But such definitions and 
distinctions can throw no light whatever on the question 
of justice in contracts. We shall see that a standard to 
be perfect need not be invariable. What is required is 
simply that it shall be dependable^ so that contracting 
parties may be able to forecast all required elements of 
their economic future in terms of that standard as accur- 
ately as in terms of any other. If a standard is thus de- 
pendable, the terms of the contract will be as "just" as 
they could possibly be under any system. 

§4. 

At a later stage the general question of " justice " will 
be discussed. Here the effort will be to show that losses 
due to " appreciation," however defined, will tend to be 
forestalled. For this, it is not necessary to scale the 
principal of a debt. The principal is not the only or 
even the chief element in a loan contract. The other 
element is the rate of interest. It is an astonishing fact 

^See, e. g., the connected discussions in the Annals of the Ameri- 
can Academy of Political and Social Science, 1892-95, and the fournal 
of Political Economy, 1893-95, by Ross, Merriam, Fetter, Commons, 
Newcomb, Cummings, Orton and Taylor. 

* See Chapter XII. 



4 A7nerica7i Economic As,sociation. [346 

that tlie connection between the rate of interest and ap- 
preciation has been ahnost completely overlooked, both 
in economic theory and in its bearing upon the bime- 
tallic controversy. 

Of the few writers who have conceived this connection, 
apparentl}^ the earliest was the anonymous author of the 
remarkable pamphlet entitled : " A Discourse Concerning 
the Currencies of the British Plantations in America." 
Boston, 1740 (Reprinted in the " Overstone Tracts," 
1857). He writes : 

The ArgU7nents current atnongst the Populace in favour of Paper 
Money, are, 

I. lu most of the Paper Money Colonies one of the principal Rea- 
sons alledged for their first Emissions ; was, to prevent Usurers impos- 
ing high Interest upon Borrowers, from the Scarcity of Silver Money. 
It is true, that in all Countries the increased Quantity of Silver, falls 
the Interest or Use of Money ; but large Emissions of Paper Money 
does naturally rise the Interest to make good the sinking Principal : for 
Instance, in the Autumn, A. 1737, Silver was at 26 s. to 27 s. per Ounce, 
but by a large Rhode Island Emission, it became in Autumn 1739, 29 s. 
per Oz. this is 7 per Cent. Loss of Principal, therefore the Lender, to 
save his Principal from sinking, requires 13 per Cent, natural Interest 
(our legal Interest being 6 per Cent.) for that Year. In Autumn A. 
1733, Silver was 22 s. per Oz. by large Emissions it became 27 s. in 
the Autumn, A. 1734 ; is 22 per Cent, loss of Principal ; and the 
Lender to save his Principal ; requires 28 per Cent, natural Interest 
for that Year. Thus the larger the Emissions, 7iatural Interest be- 
comes the higher ; therefore the Advocates for Paper Money (who are 
generally indigent Men, and Borrowers) ought not to complain, when 
they hire Money at a dear nominal Rate. 

If Bills were to depreciate after a certain Rate, Justice might be 
done to both contracting Parties, by imposing the Loss which the 
Principal may sustain in any certain Space of Time (the Period of 
Payment, upon the Interest of a Bond or Price of Goods : biit as De- 
preciations are uncertain, great Confusions in Dealings happen. 

John Stuart Mill expresses the same view,^ as do 

^ "Principles of Political Economy," Book 3, Chapter 23, \ 4. [A 
single paragraph.] 



347] Appreciation and hiterest. 5 

also Jacob de Haas^ and Professor John B. Clark.^ A 
principle which apparently has been independently dis- 
covered by each of these economists and quite possibly by 
others, is likely to be of some importance. It is the ob- 
ject of the present essay to develop the theory in a quan- 
titative form, to bring it to a statistical test, and to apply 
it to current problems, and to the theory of interest. 

^ " AThird Element in the Rate of Interest." Journal of the Royal 
Statistical Society, March, 1889. [A more extended discussion, with 
statistics.] 

2 " The Gold Standard in the Light of Recent Theory." Political 
Science Quarterly, September, 1895. [Applied to the current bime- 
tallic controvers}'.] 



CHAPTER 11. 

ONE YEAR contracts/ 

§1. 

We must begin by noting the distinction between a 
foreseen and an nnforeseen change in the value of money. 
Only the losses or gains of the former can be forestalled. 
A sudden and unexpected inflation, as in the United 
States in 1862, works enormous losses to creditors while 
an unforeseen contraction is equally harmful to debtors. 

How far foresight in such matters actually exists will 
be discussed in Part II. At present we wish to discover 
what will happen, assumiJig this foresight to exist. 

If a debt is contracted optionally in either of two 
standards and one of them is expected to change with 
reference to the other, will the rate of interest be the 
same in both ? Most certainly not. Only a few months 
ago the Belmont-Morgan syndicate offered the United 
States government the alternative of taking some 65 
millions at 3/^ in gold or at 3^/^ in "coin." Every- 
one knew that this additional ^ ^ was due to the mere 
possibility of free silver coinage. If the alternatives had 
been between repayment in gold and — not possible but 
actual — repayment in silver, the additional interest 
would certainly have been much more than 3/^ f/c . 

§2. 

To fix our ideas, let the two standards be gold and 
wheat, and, while today a bushel of wheat is worth a 

' More properly speaking, in place of "one j^ear " should be put 
" one interest interval." 



349] Appreciation and Interest. 7 

dollar, let it be known that one year hence it will be 
worth bnt 96 cents. One hundred dollars (gold standard) 
or its equivalent one hundred bushels (wheat standard) 
are borrowed today and are to be repaid with interest in 
one year. If the rate of interest in the gold standard is 
8 'fo , what will be the rate in wheat ? 

We note that the repayment, if in gold, will be, not 
$100 but $108, and our problem is solved by finding 
what will be the equivalent of this sum in wheat at the 
end of the year. This is easily obtained from the ex- 
pected price of wheat, thus : ^ 

96 cents gold =«= i bushel wheat. 

Hence i dollar " — ^i- bushels " i. e., \.o\\\>Vi. 

loS dollars " — loS X 1.04I bushels " i. e., 112^ bu. 

Thus the repayment of 1 1 2^ bushels will be equivalent 

to $108. The alternative contracts would tl\erefore be : 

\ 

For 100 dollars borrowed today, 108 dollars are due one year hence. 
For 100 bushels " " 112 J bushels " " " 

Hence 8 fo interest in the gold standard is equivalent 
to 12^% in the wheat standard. 

Now the relative change in the two standards may be 
spoken of either as an appreciation of gold relatively to 
wheat or as a depreciation of wheat relatively to gold. 
We are not compelled to inquire which is the "abso- 
lute" change. If we speak in terms of appreciation, we 
say $1 changes in value from i bushel of wheat to 1.04% 
bushels and hence has appreciated 4}i'/o ] while we may 
also say, wheat has depreciated from ^i to $.g6 or 4^. 
Our results can be stated in either of two ways : 

I. If the rate of interest in one standard is 8^, then 
in another, which depreciates 4 fo relatively to the first, 
it will be 12 }4fo ; that is, a depreciation of 4^ is offset 
by an increase of interest of 4}^ fo. 

1 The symbol " =0= " is used for " are equivalent to." 



8 American Economic Association. [350 

2. If the rate of interest in one standard is 12)^ %, in 
another, which appreciates 4 ^-^ /^ relatively to the first, 
it will be 8 ;% ; that is, an appreciation of 4 )^ ^ is offset 
by a decrease of interest of 4j^ /^. 

§3. 

Leaving this numerical case, we may state the problem 
more generally. Suppose gold is to appreciate relatively 
to wheat a certain known amount in one year. What 
will be the relation between the rates of interest in the 
two standards ? Let wheat fall in gold price (or gold 
rise in wheat price) so that the quantity of gold which 
would buy one bushel of wheat at the beginning of the 
year will buy 1 -\- a bushels at the end, a being therefore 
the rate of appreciation of gold in terms of wheat. 

Let the rate of interest in gold be z, and in wheat be 
y, and let the principal of the loan be D dollars or its 
equivalent B bushels. 

Our alternative contracts are then : 

For D dollars borrowed D-\-D i or D { i-\-i) dollars are due in one yr. 
For ^bushels " i5 f 5/ or ^ ( i+y) bushels " " " " 

and our problem is to find the relation between i and/, 
which will make the Z>(i + 2) dollars =g= the B (1 -]-j) 
bushels. 

At first, D dollars - B bu. 

At the end of the year Z> " ^ B {\+a) 

Hence " " " Z>(i+?) " =0= i? ( i-f rt) (1 + /) " 

Since Z)(i + i) is the number of dollars necessary to 
liquidate the debt, its equivalent B {1 + a) (i + 2) is the 
number of bushels necessary to liquidate it. But we 
have already designated this number of bushels by 

Our result, therefore, is : 



35 1] Appreciation and Interest. 9 

Dollars. Bushels. Buishels. 

At the end of i yearZ?(r + /) ^ B {\ -^j) = B {\ -\- a) {\ ^ i) (i) 

which, after B is canceled, discloses the formula : 

i+y=(i+«) (i+o (2) 

or j=--^^-a-\-ia (3) 

or in words : The rate of interest in the (^relatively) de- 
preciating standard is equal to the sum of three terms^ 
vis.^ the rate of interest in the appreciatittg standard., 
the rate of appreciation itself and the prodicct of these 
two elemeiits. 

Thus, to offset appreciation, the rate of interest must 
be lowered by slightly more than the rate of apprecia- 
tion/ 

We may introduce depreciation in a similar manner. 
Instead of saying, gold appreciates at the rate «, rela- 
tively to wheat, we may say, wheat depreciates at the 
rate (f, relatively to gold.^ This means that wheat has 
sunk in terms of gold in the ratio i to i — ^, and rea- 
soning similar to the foregoing shows that 

i4-^ = (i-^)(i+y). (4) 

Equations (2) and (4) may be conveniently combined, 
thus : 

i + « I i—d' ^^' 

'Professor Clark, {Political Science Quarterly, September, 1895), 
implies that i % appreciation is offset by less than i % reduction of 
interest. But in making his calculation he has failed to "compound." 
The numerical illustrations of the eighteenth century pamphleteer 
{supra) are also erroneous. E.g., instead of 28 %, should be 29.32 
%. Professor Marshall, (" Principles of Economics," Vol. T, 3rd ed., 
p. 674), gives a correct example. His example is designed to show 
the losses from a fluctuating currency and not the effort to offset these 
losses. He appears, however, to have in mind this effort when he 
postpones to the next volume the discussion of " the influences which 
changes in the purchasing power of money do actually exert on the 
terms on which loans are arranged," (p. 673). 

■■^ The relation between rfandais (i+a) (r— ^) = i, which is evi- 
dent from equation (5) or can be easily shown independently. 



lo Amej'icaji Economic Association. [352 

Since ' — is the ratio of the vahie of gold at the end 

of the year to its vahie at the beginning (all in terms of 
wheat), that is, the ratio of divergence of the two stand- 
ards expressed in wheat, while is the same ratio 

I — d 

of divergence expressed in gold, and since i + i is the 
" amount " of $1 put at interest for one year while i +7 
is the " amount " of one bushel ; we may state equation 
(5) as follows : 

The ratio of divergence betiveen the standards equals 
the ratio between their " ainoiints^ 

■ This is, perhaps, the simplest mode of conceiving the 
relation and stress is laid upon it because it brings into 
prominence the " amount," or ratio of future payment to 
present loan, a magnitude which in most questions of in- 
terest plays a more important role than the rate of in- 
terest itself/ 

Equation (5) gives the relation between i and / in 
terms of a or d. From it, follows the value of/ in terms 
either of i and a or of i and d^ and also the value of i in 
terms either of y' and a or of y' and <^, thus : 

I + ^ I 1 — a 

whence j =:i -\- a -\- i a -^ (6) 

I — d 

or i =j — d —j d ^~-^ ( 7 ) 

I -r a 

^ In fact, except for convenience in computation, the conception of 
the rate of interest might well be dispensed with, giving place to the 
conception of a year's "amount" or "ratio of accumulation." In 
his "Positive Theory of Capital," Professor Bolim-Bawerk expresses 
the same view. (English Translation, p. 296). We should then speak, 
not of a 6 % rate of interest, but of 1.06 as the " ratio of accumula- 
tion." In like manner " rate of appreciation " would give place to 
" ratio of appreciation." Denoting the ratio of accumulation, i -\- j, 
by r^ and i + ^ by r, and the " ratio of appreciation," i -p a, by />, our 

theorem becomes simply - =/>. 
r 



353] Appreciation and Interest. 



II 



It follows that j exceeds i by more than the rate of 
appreciation, which in turn is more than the rate of de- 
preciation, {i. e.^j — i^ ay> d). 

§4- 

It is to be noted that we have been regarding money 
as a standard of value and not as a medium of exchange. 
In either contract the actual liquidation need not be 
made either in gold or wheat but in some other medium, 
as bank notes. The speculator who sells wheat " short," 
really uses wheat as a standard and not necessarily as a 
medium. In consideration of value received today 
(which, though reckoned by the speculator in money, 
may readily be thought of as measured in wheat) he 
promises to deliver, at a later date, so many bushels of 
wheat, it being perhaps understood that he need not act- 
ually deliver the wheat so long as he delivers its equiv- 
alent in money. This operation, as actually practiced, 
involves great uncertainties, and therefore occurs as a 
gambling transaction. Moreover the wheat is not 
usually paid for in advance. But if wheat were a more 
reliable standard, selling it " short " in consideration of 
present advances might be a true method of business 
borrowing, and would then exactly exemplify the case 
we have supposed. In fact, such contracts are identical 
in form with those which would be made under the 
oft-proposed " multiple standard." 



CHAPTER III. 

MORE THAN ONE YEAR. 
§1. 

A prominent bimetallist in conversing with the writer 
on the subject of interest and appreciation, raised the 
following objection: "Interest and principal are sepa- 
rate ; the one is paid regularly in installments ; the other 
remains to the end ; hence appreciation must affect them 
in totally different ways. I do not see how it is possible 
by a uniform reduction in interest applied to contracts 
of different periods to offset the appreciation of both 
interest and principal." This view, as we shall soon 
see, is quite erroneous and arises from the habit of 
separating in thought interest and principal. 



First consider the case in which no interest is paid 
until the end of the term of years. Let us suppose, 
for instance, a savings bank which receives $ioo, gold 
standard, and repays the depositor in five years at 5 ^ 
compound interest. If there were an alternative 
standard, say wheat, in terms of which gold is known to 
appreciate ^ constantly by i ^ per annum, what would 
be the rate of interest in this standard ? We shall sup- 
pose for convenience that at first the price of wheat is 
$1 per bushel. 

^ Or what is equivalent, wheat depreciates ygx^ relatively to gold. 
As it will be understood that there are always these two modes of ex- 
pressing the relative change of two standards, we shall hereafter 
adhere to "appreciation." 



355] Appreciation and Interest. 13 

If the repayment were to come in one year, we know 

from Chapter I, § 3, that the rate of interest in wheat is 

given by the formula 

j^i-{-a-\-ta 
= .05 + .01 +.0005 
= .060^ 

This result is as truly the answer to our problem for a 
series of years as for one year. The proof consists 
simply in separating the contract into several contracts 
of one year each. Thus, by Chapter II, we know if we 
deposit today 1 100 or its equivalent, 100 bushels, it will 
amount in i year to $105 at 5;^ or its equivalent, 106.05 
bushels, at 6^^o. We may now regard these equiv- 
alent amounts as withdrawn but immediately redeposited 
for one year. Then, with the same rate of interest in 
gold and the same rate of relative appreciation, we shall 
obtain the same rate of interest in wheat, so that $105.00 
or its equivalent, 106.05 bushels, will amount in i year 
to I110.25 ^t 5^, or its equivalent, 112.47 bushels at 
6-^^. In this way each successive pair of " amounts," 
including the last, will be equivalent. 



The principle employed in § 2 is to resolve the contract 
into a series of one year contracts. The general case is 
precisely similar. For the first year we have, by 
formula (i). Chapter II, 

Dollars due. Bushels due. Bushels due. 

D{i + i)<^B{i+j)=B{i + a){i-\-i) 

In the second year the same formula applies except 
that in place of Z?, the principal is now Z> (i + 2), and 
in place of B, B (i +/) or ^ (i + a) (i + i). Making 
these substitutions in the formula, we obtain 



l>[\ iV -^ /.\i , ,/y /*(i I aY [i ! i'Y 
A\\<\ similuK in tlu- thli\l year, 

aiul sv» vMi. Kach of the results discloses the priuoiple 

1\\ §$ J i\iv*.l ^^> we began for simplicity with the case 
in which the debt is allowetl to accmuulate to the end. 
The most general ease, however, is one in which the re- 
|x^yn\ents are in installments. 

Suppose, as in § 3, that the interest in gold is 5 '/c and 
that gold is known to appreciate i % per annum rela- 
tively to wheat. A fanner mortgages his land for $i.ckx> 
oar its then e<jnivaleut, i>ooo bushels of wheat, and agrees 
to pay annually the interest and such parts of the principal 
as he can save, tnaking the repayment complete in 7 years. 
Our problem is to find that rate of interest in wheat 
which will make the contracts in gold and wheat 
e<^uivaleut iu every respect. 

The solution of this problem is precisely the same as 
that of § 2, viz., 65^ %, For. at the end of one year, the 
farmer's debt amounts to $1050 or its then equivalent, 
io6<X50 bushels, Let us suppose that he finds himself 
aUeto pay, not only the ^4nterest>" $50, but also $50 of 
the ^' principal,' * that is $100 altogether. The equi\^ 
lent of this iu wheat is ici. 00 bu. 

Hence he cart either 

pay $ic>o,<x> oa $1,050,00, leavnng $95aoo 

or 101,00 bu, Qu. 1,060^50 bu., leaving 959^ 50 bn. 
aod, since the ^"amounts" $1,050 and 1,060,50 bu, are 
e^ilu\^ilent and the deductions; $ioo and ioi,oo bu, are 



557] 



Appreciation and Interest. 



15 



equivalent, the remainders $950 and 959.50 bu. must also 
be equivalent ; and, in fact, this may be seen directly 
since, with gold appreciating i ^ , $950, originally worth 
950 bu., becomes worth i ^ more, or 959.50 bu. 

Thus the farmer's remaining debt at the end of the 
first year is the same whether measured in wheat or 
gold and since the same reasoning applies to the second 
year, third year, etc., the equivalence remains to the end 
of the contract. 

It is worth noting here that the $100 payment in gold 
will be regarded as consisting of half interest and half 
principal, whereas the equivalent payment in wheat, 
101.00 bu., consists of 60.50 bu., interest and 40.50 bu., 
principal. 

The liquidation of the contract during the 7 years 
may be supposed to take place in either of the following 
equivalent ways : 

GOLD STANDARD. 





I 
Interest. 1 Amount. 


Paj-ment. 


Prixicipal. 


At beginning 






|i,ooo.oo 
950.00 
900.00 
800.00 
690. 00 

550.00 

300.00 
0.00 


In I year 

In 2 years 

':\i ■::■:■:■. 

"6 " 

"7 " 


I50.00 
47-50 
45.00 
40.00 
34-50 
27.50 
15.00 


^1,050.00 
997-50 
945.00 
840.00 
724-50 
577-50 
315-00 


|ioo.oo 
97-50 
145.00 
150.00 
174-50 
277-50 
315-00 



WHEAT STANDARD. 





Interest. 


Amount. 


Paj-ment. 


Printripal. 


At beginning 








1,000.00 bu. 


In I year 

In 2 years 

"3 " 

"4 " 

'•5 " 

"6 " 

"7 " 


60.50 
58.05 
55 54 
49-87 
43-44 
34-97 
19.27 


1,060.50 
1,017-55 
973-63 
874- 1 1 
761.46 
61303 
337-73 


101.00 
99.46 

149-39 
156.09 
183.40 
294-57 
337-73 


959-50 " 
91S.09 " 
824.24 " 
718.02 " 
57S.06 " 
318-46 " 
0.00 " 



In these two tables ever}- entrs" in one is equivalent to 



i6 American Economic Association. [358 

the corresponding entry in the other except those in the 
interest columns. 

We thus see that the farmer who contracts a mortgage 
in gold is, if the interest is properly adjusted^ no worse 
and no better off than if his contract were in a " wheat " 
standard or a " multiple " standard. 

§5- 
The principle involved in § 4 is that equivalent pay- 
ments subtracted from equivalent " amounts " will leave 
equivalent remainders. The payment in any year forms 
the same fractional part of the " amount " in the two 
standards. We may designate this fraction at the end 
of the first year by y^ the second year by _/', etc., and 
we have the following results : 

END OF FIRST YFAR. 
Dollars. Bushels. Bushels. 

Amount. i?(i+/)* ^(i+y)= ^ (1+^) ( i-|./) 

Paym't f D {\^i) -^ fB{i-^j) = f B { \ ^a ) (i+z) 

R'md'r . (I-/) Dii^i) <^ (i-/) B{i^j ) = (i-/) B{x^a) (1+/) 
In like manner the unpaid remainder at the end of the 
second year can be shown to be 

Dollars. Bushels. Bushels. 

(I-/') (I-/) D (1+0= * (I-/') (I-/) B (i+y)2= (I-/') (I-/) B (i+ar- (1+02 

and so on for any number of years. Each result again 
yields the formula (i +/) = (! + «) (i + z). 

This includes, of course, the case of § i, in which no 
partial payments are made,y^y"', etc., being then zero. 

§6. 

One special case may seem to require separate consid- 
eration. Suppose the interest alone is annually paid and 
the principal redeemed at the end, as in the case of a 
bond not subject to a sinking fund. What correspond- 
ence between the two standards is then possible ? The 
following tables answer this question, the first, for the 



359] 



Appreciation and Interest. 



17 



case where the wheat interest, the second, where the 
gold interest is annually paid. 



TABLE I. 



TABI,E II. 





Interest. 


Amount. 


Payment. 


Principal. 


At beginning (Bushels^ 








1,000.00 


In I year . . . ' 


• 


60.50 


1,060.50 


60.50 


1,000.00 


" 2 years. . 


















" 3 " 




















«' 4 '« 
" 5 " 




















« 6 << 




















" 7 " 
" 8 " 
" 9 " 












' 








" 10 " 
















1,060.50 


0.00 


At bep^inning (Doll^i's^ 








1,000.00 


In I year . . . ' 


' 


50.00 


1,050.00 


59-90 


990. 10 


' ' 2 years . . 






49-50 


1,039.60 


59-31 


980.29 


" 3 " 


. 






49.01 


1,029.30 


58.72 


970.58 


" 4 '• 








48.53 


1,019.11 


58.14 


960.97 


" 5 " 








48.05 


1,009.02 


57.56 


951.46 


" 6 " 


. 






47-57 


999.03 


56.99 


942.04 


" 7 " 








47.15 


989.19 


56.43 


932.76 


" 8 " 








46.63 


979-39 


55.87 


923.52 


<< g .< 








46.17 


969.69 


55.32 


914.37 


" 10 " 


• 






45-71 


960.08 


960.08 


0.00 



At beginning (Busi 
In I year . . . ' 


lels) 






1,000.00 


60.50 


1,060.50 


50.50 


1,010.00 


" 2 years. 






' 61.10 


1,071.10 


51.00 


1,020.10 


"3 " • 






' 61.72 


1,081.82 


51.52 


1,030.30 


"4 " . 






62.32 


1,092.62 


52.03 


1,040.59 


"5 " • 






' 62.96 


1,103.55 


52.55 


1,051.00 


"6 " . 






63.59 


1,114-59 


53-08 


1,061.51 


"7 " . 






' 64.22 


1,125.73 


53-61 


1,072.12 


"8 " . 






64.86 


1,136.98 


54.14 


1,082.84 


"9 " . 






65.51 


1,148.35 


54.68 


1,093.67 


" 10 " . 






66.17 


1,159.84 


1,159.84 


0.00 


At beginning (Del 
In I year . . . ' 


lars) 






1,000.00 


' 50.00 


1,050.00 


50.00 


1,000.00 


" 2 years. 
"3 " • 
"4 " . 
"5 " • 
"6 " . 








< 








"7 " . 
"8 " . 
















"9 " . 
















" 10 " . 






( (( 




1,050.00 


0.00 



1 8 America7i Economic Association. [360 

From Table I, it will be seen that the case in the 
wheat standard, in which only the interest is annnally 
paid and the principal redeemed in ten years is equiva- 
lent, step for step, in the gold standard to a series of 
small partial payments. Thus, instead of paying merely 
the annual interest of I50, the sum paid the first year is 
$59.90 reducing the principal by $9.90. At the end 
there is due I914.37 of principal and $45.71 of interest, 
making $960.08 in all, which at that date is, of course, 
precisely equivalent to the 1,060.50 bushels, the final 
payment in wheat. 

On the other hand, the case in which the gold interest 
payments are kept up, corresponds to a series of wheat 
payments less than the annual interest, so that the un- 
paid interest accumulated to the end makes the sum then 
due, 1,159.84 bu., of which 1,093.67 bu. are principal. 

It is thus clear that the case in which in one standard 
the interest is paid annually and the principal at the 
end, can be exactly matched in the other standard either 
by minute partial payments or minute arrears of interest. 
Without such partial payments or arrears in one of the 
standards, the two would not be equivalent step for step. 
We shall see, however, that they would still be equiva- 
lent as a whole. 



CHAPTER IV. 

" PRESENT VAI^UE." 



In practice, of course no such minute partial payments 
of principal or minute remissions of interest would be 
made. Any advantages to be derived from such calcula- 
tions of trifles would not be worth the trouble. But 
even if we destroy the precise step-for-step equivalence 
between the wheat and gold tables, we do not destroy 
their equivalence as a whole. The '•^present values " 
remain exactly equal. 

The ordinary definition of the " present value " of a 
given sum due at a future date is " thai sum which put 
at interest today will ' amount ' to the given sum at 
that future date." " Present value " and " amount " are 
thus correlative terms. In fact we may extend the pre- 
ceding definition to include the present value of past 
sums as the accumulated " amount " today of the past 
sum put at interest then. 

The literal meaning of " present value " implies that 
it is the actual market price today of a future sum due. 
This is, in fact, the case. We need not stop to prove it 
in theory, for we are all familiar with it in practice. 
Elaborate tables are constructed on this principle for the 
practical use of insurance companies in calculating their 
premiums, and for brokers in determining the compara- 
tive merits of various bond investments. What we are 
here concerned with is applying the principle to our 
problem. 



20 A7ficrican Ecoyiomic Association. [362 

§2. 

If a debt of $1,000 is contracted today, interest being 
5^, the "present value" of all payments, principal and 
interest, by which that debt is to be liquidated is exactly 
$1,000.^ Again, the debt's present value, reckoned at a 
later date than the time of contract, is the " amount " of 
$1,000 at interest from the time of contract to that date, 
and this is true, whether or not any of the debt has al- 
ready been paid. Thus if the present values at the date 
of contract are computed for the gold and the wheat 
debts of the last chapter, they will be $1,000 and 1,000 
bushels, which are then equivalent. If the present val- 
ues one year later are taken they are $1,050 and 1060.50 
bushels which at that date are also equivalent, gold hav- 
ing appreciated i fo . 

From these familiar principles, it follows that the 
present values of the two debts, reckoned at any date 
whatever, are identical whether the individual payments 
correspond or not. Thus, to take the case first referred 
to, suppose the wheat debt to be discharged as in Table I 
and the gold debt, as in Table II. The present value, at 
the date of contract, of the interest and principal, sepa- 
rately computed, will be •? 

Dollars. Bushels. 

Present value of all interest payments . . . , 386.09 < 444.24 

" " principal due in 10 years . . 613.91 > 555.76 

" " total 1000.00 "^ 1000.00 

If the present values (including " amounts " of past 

' This and the other general theorems on present value are not proved 
here because their proof is accessible in most treatises on interest, an- 
nuities, insurance, etc. See, e.g., the "Encyclopaedia Britannica," 
" Annuities." 

'^ The symbol < is here used for "is less than the equivalent of " 
and > for "is more than the equivalent of." 



363] Appreciatio7i and Interest. 21 

interest) were computed 5 years after the date of the 
contract, the items would be : 

Dollars. Bushels. 

Interest 492-75 < 595-88 

Principal 783-53 > 745-5° 

Total 1276.28-1341.38 

We thus see that it would be just as much a hardship 
to pay the high interest in wheat as to pay the more 
onerous principal in gold, 

§3- 

The case of a perpetual annuity may be given special 
consideration. As is well known, the present value of a 
perpetual annuity is its " capitalized " value. Thus, if 
the rate of interest is taken at 5 ^ , the present value of 
a perpetual annuity of $50 per annum is $1,000. Ap- 
plying the same principle to the wheat annuity of 60.50 
bushels and extending the previous reasoning, we find 
that the two annuities are equivalent. 

At first sight this seems impossible since 6-^ ^ is a 
higher rate of interest than 5^. This is true in the 
numerical sense, and it is also true that the early pay- 
ments of 60.50 bushels are actually more valuable than 
$50. But after a certain time (in this case 19 years) the 
reverse is true. The 19th payment of $50 in gold is 
worth 60.40 bushels while the 20th is worth 61.01 bush- 
els. That is, the recipient of the wheat annuity has at 
first a slight advantage over the recipient of the gold 
annuity which ceases and becomes a slight disadvantage 
after 19 years. 

§4. 

To derive the formula for the time at which the rela- 
tive values of the two annuities become reversed, let the 
rate of interest in gold be z, in wheat,/; let the two an- 



22 American Economic Associatio7i. [364 

nuities be D i and B j^ their capitalized values being D 
and B [D =c= ^ at the beginning) and let x be the num- 
ber of years in which BJ is as valuable as or more val- 
uable than D i. Then 

Bushels. Dollars. 

At end of x years, - - - B j > Di 
At end of .r + i years, - B j < Di 

and since we know that in x years, D ^ B {\ ^- a)' and 
hence Di o- Bt(i ^ a)'] and likewise in .r + i years, 
Di =0= B i{\ + cl)""^^ ^ we see that the previous inequal- 
ities become : 

Bushels. Bu.shels. 

At end of x years, - Bj > Bi(i ^ aY 
At end of ;i; + i years, Bj < Bi{i -\- <^)-^+ ' 

which may be combined in the formula : 

i (i +aK^y <i (i +«)^+ I 

^<log/^log^ ^_^^_ (8) 

— log(i+a) 

That is, X is the integral part of the number 

log J — log t 

log (I +«)■ 

Thus, if 2^.05, a = .01, and hence also/ =.0605, 

then 

logy — log z_ 2.7818 — 2.6990 .0828 

log ( I + a) .0043 "~ .0043 ~ 

Hence x = ig. 



CHAPTER V. 

VARYING RATES OF INTEREST AND APPRECIATION. 

§1. 

Hitherto we have assumed that the appreciation pro- 
ceeded (during the period of the contract) at a constant 
percentage rate per annum, and that the rate of interest 
(in one standard, and consequently in the other) remained 
constant also. The more general case is one in which 
these elements are changing. 

Beginning with a numerical case, let us suppose that 
the United States government is offered an alternative 
loan, not in gold or " coin," but in gold or silver. Let 
it be known that lOO gold dollars will remain at par the 
first year, but in two years will be worth 150 silver dol- 
lars, that is, gold will " appreciate," in the second year, 
50 ^ relatively to silver ; also that in the third and 
fourth years it will appreciate 10 fo and 5^ respectively. 
We shall suppose that the rate of interest, if the con- 
tract be in gold, is 3 ^ for each year of the contract. 

Our problem is to discover what will be the interest 
in silver. It is perhaps already evident that it will be a 
different rate for each year. If the contract were made 
for one year only, the rate of interest in silver would 
also be 3 ^ , since silver remains so far at par with gold. 
If the contract (or any unpaid part of it) were then re- 
newed for a second year, the rate of interest would be, 

by formula (3) : 

j = z -\- a-\- ai 
= .03 + .50 + -015 
= .545 

= 54i% 



24 American Economic Association. [366 

In like manner, we may deduce the rate of interest in 
each year, with the following results : 

Gold Silver Appre- 

Standard. Standard. ciation. 

istyear ...... 3% 3 % 0% 

2d year 3 54^ 50 

3d year 3 13^ 10 

4ttiyear 3 SyVj 5 

Etc. 



The question arises, can a single " average " rate of 
interest be substituted for the above irregular series ? 

We answer that such an average is not possible if the 
debtor has the option of arbitrary partial payments. 
If, for instance, the average were 20^, and the govern- 
ment could pay ofi at any time, it would evidently be 
tempted to refund the debt at the end of the second 
year, to which the lending syndicate would not agree. 
If, however, the conditions as to repayment are stipulated 
for in advance, an average can easily be computed on the 
principle of present values. 

Suppose the government agrees to extinguish the 
debt in four years by paying at the end of successive 
years 20, 40, 30, and 10 millions (these to include " in- 
terest "). The present value of these sums is 66.321 
millions, which is therefore the amount of the loan re- 
ceived from the syndicate. This sum is obtained by 
adding the present values of several payments. The 
present value of 20 millions, due one year hence, is 

^° = 19.418 millions. 
1.03 



and of 40 millions, due two years hence, is 

• ~ = 25.136 millious, 

(1.03) (1.545) 

for evidently if this be put at interest for one year at 



367] Appreciation and Interest. 25 

3^, and the next at 541-% it will amount to 40 millions. 
Likewise the third and fourth payments have present 
values of 

-. ,, ^° ,, r = 16.639 millions 

(i.03)(i.545)(i.i33) 

5.128 millions. 



(i.03)(i.545)(i.i33)(i.o8i5) 



The sum of these four present values is 66.321 mil- 
lions. Now if we compute the present values of the 
four payments on the basis of a uniform rate of 20.26% 
interest, we obtain the same sum, thus 

r= 16.631 millions 



(1.2026) 



40 



(1.2026^ 
30 



27.659 



^ = 17-250 
( 1. 2026)'' 

^° = 4-781 " 
(r.2026)* 

Total, =66.321 " 

The separate present values are here fictitious, that is, 
no one of them is the actual present selling price of the 
future payment to which it refers, but the deviations so 
offset each other that their sum is the actual present 
selling price of the whole set of future payments. It 
follows from principles already stated that the debt, 
66.321 millions, can be liquidated by precisely the same 
payments (20, 40, 30 and 10 millions) whether the in- 
terest is reckoned separately at 3, 54^, i3to", ^^^ ^tot^ 
or uniformly at 20.26%. In fact the details of the book- 
keeping in the two cases are : 



26 



American Economic Association. 



[368 





At 3, 54i i3T^ff. StVc^- 


At 20.26% uniformly. 




(In Millions.) 


(In Million.?.) 




I'^ter- ^^o„„t 


Pay- 
ment. 


Prin- 
cipal. 


Inter- 
est. 


Amount. 


Pay- 
ment. 


Prin- 
cipal. 


Date 

In I year . 
In 2 years . 
In 3 years . 
In 4 years . 


1.99, 68.31 

26.33 74-64 

4-6i 39 25 

.75 10,00 


20.00 
40.00 
30.00 
10 00 


66.32 
48.31 
34-64 

9-25 
0.00 


13-44 
12. II 

645 
1. 68 


79-76 
71.87 
38-32 
10.00 


20. on 
40.00 
30.00 
10.00 


66.32 

59-76 

3t-^7 

8.32 

0.00 



We thus see that 20.26^ is the "average" of 3, 54^, 
133^ and S^^^^s in the sense that, by it, the same pay- 
ments will cancel the same debt. It is not identical 
with the arithmetical average, which is 19.74^. 

§3- 

Let ns suppose that the rate of appreciation of one 
standard in terms of the other is foreknown to be a^ the 
first year, a.^ the second year, a., the third year, and so 
on ; also, to be as general as possible, that the rates of 
interest in both standards are variable, being in the ap- 
preciating standard i^ the first year, i., the second, etc., 
and in the depreciating standard, y^, y^, etc. Let the 
final settlement occur in n years. Then, as in § 2, we 
may regard the contract as equivalent to a series of one- 
year contracts successively renewed in whole or in part, 
the difference being only that the terms are all made in 
advance. As equation (2) applies to each of these con- 
tracts, we have 

I +yx =(! + «,) (! + ?■,) 



(9) 



To obtain an expression for the average rate of inter- 
est in either standard, i. <?., z „ (ory J, we require a given 
series of payments Z?^, Z>^, . . . Z>„ in the gold standard 



369] Appreciation and Interest. 27 

(or their equivalent B^, B.^^ . . . B^^ in the silver 

standard). The aggregate present value of these 

payments, reckoned by the separate rates of interest, 
^i^'^2^ . ■ iiorjnJ, . . yjis 



l+i, ' (I + i,) ( I + /J ^ ^ (I + Zj (I + tj . . . (I + 4) 

(or the corresponding expression in terms of j^'sand/'s). 
Now the " average " rate i ^^ must be such that if applied 
to the same set of payments it will make the same sum 
of present values ; that is, i^ is determined by 



1 + 4 ' (1 + 4)- ' (i + 4r 

(10) 

i + 4^(i + 4)(i + 4)^ ^(i + 4)(i + /j • • (i+?j 

and j\^ is determined by the corresponding formula in 
^'s and y 's. 

This equation has only one real and positive root or 
value of i ^. It can readily be obtained by Horner's 
Method/ We shall call z^ and /^^ the "actuarial aver- 
age" of ?„ ?„ • . z; and of /„ /„ . . /„ re- 
spectively.^ 

' For, h\ substituting for -, the single letter x and for 



1 + 4 I + 4> 

, etc., the letters x^, .tr„ etc., the equation becomes : 

1 + 4 

D^x + D^x""-^ ■ ■ +D^x'^ = D^x^-{-D^x^x^+ . ■ +D^x^x^ . . x^. 
In the example of I 2, the equation becomes : 

20 .ar + 40 ;r^ + 30 .ar^ + ID .ar* = 66 321, 
the required root of which is x = .83155, 

which, applied to ^^ , gives j\^=^ .2026. 

I+7a 

* I + 4 reduces to the "geometrical average " of i + 4» i + 4) ^^c. . 
when Z?, = Z>, = . • = D.-, = o. 



28 American Economic Association. [37° 

§5. 

We may define tlie average rate of appreciation of one 
of the two standards in terms of the other as that rate 
which would connect the two average interest rates if 
the latter were actual (instead of averages of actual) rates. ^ 
That is, the average appreciation, a,_^^ is given by the 
equation 

or a -^iiJZ^? (11) 

Thus in the example of §1, the average silver interest 
is 20.26^ and gold interest 3^ so that 

.2026 — .0^ r„i, 

«a= , = ■ 1676, 

I + .03 
or 16.76^. This average is not identical with the 
arithmetical average of o, 50, 10 and 5^s, which would 
be 16.25%, ^^*^^ i^ it identical with that rate which if 
uniform would result in four years in the same diver- 
gence between silver and gold as was produced by the 
four successive rates o, 50, 10 and 5/^s; this would be 
14.70%. For the statistical purposes of Part II., how- 
ever, the latter method is adopted for simplicity and is 
doubtless correct within the limit of error. 

§ 6. 

It may seem that the subject of this chapter can have 
no practical application. In Part II we shall see that 
this is not the case. A government bond, for instance, is 
a promise to pay a specific series of future sums, the 
price of the bond is the present value of this series and 

^ It may be proved that this definition of a^, satisfies the general 
condition of au average, viz., that a^ reduces to a,, a^, etc., when the 
latter are all equal, whether z,, i^, etc. {and j\.j\, etc.,) be all equal 
or not. 



37 1] Appreciatio7i and hiterest. 29 

the " interest realized by the investor " as computed by 
actuaries is nothins: more nor less than the " averao-e " 
rate of interest in the sense above defined. Of course 
the investor puts no specific values on the individual 
yearly rates of interest of which the "interest realized " 
is the average, but that this interest is truly an average 
is attested both by the comparative stability of the rate 
of interest realized on long time bonds as compared with 
the fluctuations of the rate of interest in the short time 
money market ( a stability which the rate realized on the 
bonds does not possess when near maturity^ ) and by the 
fact that interest realized on a very long bond, say 50 
years, is often lower than on a 25 years' bond. This is 
explainable by the prevailing opinion that interest tends 
to fall, so that if the 50 years' investment were in two 
successive bonds of 25 years each, the interest realized 
in the second would be lower than in the first. The 
" actuarial average " of the two is equal to the interest 
realized on the 50 years' bond. 

' This is abundantly verified by market quotations, as is also the 
fact that the interest realized to him who buys a bond and sells it 
again in a short time is even more variable than rates on money. 
Thus, if in a fortnight ( in which no interest falls due ) the bond ad- 
vances y%, the speculator realizes at the rate of about 3% per annum ; 
if the rise is %, he realizes over 12%. The investor who holds a bond 
along time realizes an interest which is an "average " of the oscillat- 
ing rates of those who speculate during the interim. 



CHAPTER VI. 

ZERO AND NEGATIVE INTEREST. 



Having established the truth and generality of the 
principle i +/ = ( i + <^) (i + z"), we next inquire what 
limits, if any, are imposed on the three magnitudes 
y, rt-, i. The foregoing equation seems to require that, 
when the appreciation is sufficiently rapid, the rate of 
interest in the upward moving standard should be zero 
or negative. Thus if a =j\ the equation gives us i= o. 
iVgain if « >y then z < o. For instance, if /, the rate 
of interest in wheat, is 8 ^ and if gold appreciates rela- 
tively to wheat 20^/0 per annum, we have i -J- .08 := 
(i + .20) (i + i) whence i= — .10 ; that is, the rate of 
interest in gold would be minus 10 fo I 

Now it is clear that negative interest is impossible. 
Any possessor of $100 of gold (or its equivalent in goods 
which can be sold for gold) would hoard the gold rather 
than lend it at a loss. That is, the relation z < o is im- 
possible and therefore also « >/ is impossible. Thus 
our magnitudes are restricted within certain limits, viz., 

z > o 

(12) 

or, in words, the rate of interest in a money which can 
be hoarded (without trouble, risk or expense) can never 
sink below zero and the money itself can never undergo 
an expected appreciation (relatively to another standard) 
greater than the rate of interest in that standard. 



373] Appreciation and Interest. 31 

§2. 

This last result will not seem mysterious when we re- 
flect that the same cause, viz., hoarding, which prevents 
the interest from being negative also checks the expected 
rate of appreciation. An example will make this clear. 
It is a familiar fact that the expected rate of appreciation 
of real estate (relatively to money) can never be more 
rapid than the rate of interest (in money). If the latter 
is 5^, the (money) value of land can never advance 
faster than 5 ^ per annum except when that advance is 
unforeseen. 

The explanation is simple. If it were foreknown that 
certain land values would rise 10^, owners would be 
able to make twice as much by holding as by selling 
and investing the proceeds at 5^. The land would be 
hoarded. This decreases the supply and sends up the 
price until it is within at least sfooi the expected sell- 
ing price one year hence. It thus happens that holding 
city lots for speculation comes to be regarded as a regular 
investment from which the same return is to be ex- 
pected as from investing in a productive enterprise. The 
same could be said of wheat, cotton, or other specula- 
tion. Hoarding money is but a particular form of 
"holding for a rise." In all cases the process tends to 
lessen the rise — not to obliterate it but to make it equal 
to the rate of interest (in the standard in which the rise 
itself is measured). 

In the case of appreciating money we saw that, of the 
two conditions i~ o and a ^j\ the first was the more ob- 
vious, while in the case of appreciating real estate the 
second was the more obvious. The reason is that in 
both cases we are accustomed to think in terms of 
money. We say, " the rate of interest cannot be nega- 



32 American Economic Association. [374 

tive," " the expected rise of real estate cannot exceed 
the rate of interest," but, as we have seen, each of these 
statements implies another. It may strike the reader as 
a new idea that land speculation presents an actually 
existinp- case of zero interest. And yet this is undoiibt- 
edlv so, if we take as our standard an acre of speculative 
land. The land speculator is " making money " but not 
" making land." His 100 acres remains 100 acres. We 
could even imagine all loan contracts translated from 
" dollars " into " acres " (though still keeping money as 
the mcdiitni). K debt of 100 " acres " would be liquid- 
ated one year hence by 100 " acres " and interest would 
be nil. There is no intrinsic reason why this same zero 
interest (for absolutely safe loans) might not sometime 
be true of money, and this without implying any change 
in the abundance of capital. 

§3. 

It is important to emphasize the fact that these limits 
imposed on the magnitudes i and a come from the possi- 
bility of hoarding money without loss. If the money were 
a perishable commodity, such as fruit, the limit would be 
pushed into the region of negative quantities. One can 
imagine a loan based on strawberries or peaches con- 
tracted in summer and payable in winter with negative 
interest.^ Or, again, we may define a " dollar" as con- 
sisting of a constantly increasing number of grains of 
gold.^ If the weight doubles yearly, such " dollars" 
cannot be hoarded without growing fewer with time, 
and if interest was previously 5 ^ it will now be minus 
^iVz^oy for he who borrows $100 (2580 grains) to-day 

iCf. Bolim-Bawerk, " Positive Theory of Capital," pp. 252, 297. 
2 Such a definition for either the gold or silver " pound" is implied 
in Professor Foxwell's proposal for a " climbing" ratio. 



375] Appreciation a^id Interest. 33 

will pay back I52.50 (2709 grains) one year hence. 
Again we find a real example by recurring to land 
speculation. Since to hold land usually involves paying 
taxes upon it, the rate of interest in terms of such 
" acres" is often, in actual fact, negative. 

§4. 

In this connection, an apparent difficulty needs to be 
explained. If gold should appreciate up to the maxi- 
mum limit so that the interest rate were zero for safe 
loans, would not all investment cease ? What object 
would a capitalist have in investing when he could gain 
as much by hoarding ? Nothing could be more natural 
than the fallacy here involved and we ought not to be 
surprised on finding it among the arguments of certain 
bimetallists. For example, the Free Coinage Conven- 
tion at Memphis, Tenn., a year ago, adopted the follow- 
ing resolution : " The demonetization of either silver or 
gold means a fall in the prices of commodities, a dimi- 
nution of the profits of legitimate business, a continuing 
increase in the burden of debts, with consequent hard 
times, idle labor and idle capital., the increasing value 
of money promising a surer rettirn to a hoarded dollar 
than to an invested oney 

The error here contained is the ancient confusion of 
capital and money. It is true that a limited^ amount 
of gold would be withdrawn and hoarded, but this 
would not check the investment of capital any more 
than the similar withdrawal of so much copper. If a 
hoarded dollar yields a " sure return," a hoarded dollar^ s 

' As in the case of land, the hoarding would reach its limit when it 
had raised the value (marginal utility) of present money up to the 
present value of future money. Hoarding beyond this point would 
bring loss. 
3 



34 American Economic Association. [.37^ 

worth of goods as surely bri?tgs loss. The possessors of 
stocks of cotton or grain, machinery or ships, the prices 
of which are falling, have no disposition to keep them 
unemployed. A retail dealer fills his store with carpets 
and gives the wholesale dealer his note for three months. 
He is said to borrow " money" but he really borrows 
carpets. He may pay no (money) interest and yet the 
wholesaler gains by the loan. He is saved a loss in the 
(money) value of the carpets which he would have in- 
curred had he failed to get rid of them. In terms of 
carpets he may be making 5^. Similar considerations 
apply when the loan is negotiated through a third party, 
as a bank, and apply in fact to all forms of loans and 
investments. But the case supposed is so highly hypo- 
thetical and the error involved has been so often ex- 
plained ^ that no further treatment of it seems necessary 
here. However turned or twisted and from whatever 
point of view examined, lending " money" at no per 
cent, may under certain circumstances be a very profita- 
ble transaction. It goes without saying that the fore- 
going conclusions apply only to " pure" or " net" 
interest. That part of market interest representing 
risk, and that part representing commissions for transact- 
ing the business of lending and borrowing would not 
disappear. 

^E. g. F. A. Walker, "Money.." (New York, 187S), p. 94. 



PART II. FACTS. 
CHAPTER VII. 

INTRODUCTION. 



No study of the relation between appreciation and in- 
terest would be complete without verification by facts. 
In imaginary illustrations, such as those used in Part I, 
it is easy to make calculations agree to the last decimal 
place ; but the figures in which we are really interest- 
ed must come from actual market quotations. Through 
these alone can we test our assumption that foresight in 
regard to the appreciation or depreciation of money ac- 
tually exists. 

At the outset the question arises, how can a merchant 
be said to foresee the appreciation of money ? Appreci- 
ation is a subtle conception. Few business men have 
any clear ideas about it. Economists disagree as to its def- 
inition, and statisticians as to its measurement. If you 
ask a merchant whether he takes account of appreciation, 
he will say he never thinks of it, that he always regards 
a dollar as a dollar. Other things may change in terms 
of money, but money itself he is accustomed to think 
of as the one fixed thing. But though we do ordinarily 
regard the value of a dollar as a fixed magnitude, this 
does not really prevent our taking account of its changes. 
In our daily life we think of the earth as fixed, but we 
virtually take account of its rotation whenever we speak 
of sunrise or sunset. During a period of inflation the 
ordinary man conceives the premium on gold as a rise of 



^6 American Economic Association. [378 

gold not a fall of money. But if he takes account of 
rising wages and rising prices he arrives at the same re- 
sults as if he had thought of falling money. We need 
not ascribe to the practical man any knowledge of 
" absolute " appreciation, but whatever absolute apprecia- 
tion is, it is included, though unseparated, in the practical 
man's forecast in terms of money of all the economic 
elements which concern him — prices of his product, 
cost of living, wages of his workmen, and so forth. If 
he expects falling prices and rising wages, as is often the 
case, he may be said to foresee an appreciation of gold 
as defined by the ordinary bimetallist and at the same 
time a depreciation as measured by difficulty of attain- 
ment. What is more, he takes account of the relative 
importance, as affecting himself, of the various changes 
which he expects, and not of their relative importance 
in the elaborate averages of the statistician, averages 
which may emphasize some commodity or some labor 
whose fluctuations have absolutely no concern for him. 
His effort is not to predict the index numbers of Sauer- 
beck or Conrad, but so to foresee his own economic fu- 
ture as to make reasonably correct decisions, and in par- 
ticular to know what he is about when contracting a loan. 
If gold appreciates in such a way or in such a sense that 
he expects a shrinking margin of profit, he will be cau- 
tious about borrowing unless interest falls ; and this very 
unwillingness to borrow, lessening the demand in the 
" money market," will bring interest down. Further 
explanation of this process is postponed to Chapter X. 



Before proceeding to specific statistics, it is important 
to emphasize the broad fact that in general, business fore- 
sight exists and that the accuracy and power of this fore- 



379] Appreciation and Interest. 37 

sight is greater today than ever before. It is one of the 
distinguishing marks of modern business. Multitudes 
of trade journals and investors' reviews have their sole 
reason for existence in supplying data on which to base 
prediction. Every chance for gain is eagerly watched. 
An active and intelligent speculation is constantly going 
on which, so far as it does not consist of fictitious 
and gambling transactions, performs a well known 
and provident function for society. Is it reasonable 
to believe that foresight, which is the general rule, has 
an exception as applied to falling or rising prices ? Or, 
if so, can the academic bimetallist assume himself pos- 
sessed of a foresight of which he says the practical man 
is incapable ? It is the practical man's business to fore- 
see. It is he who first gathers the facts and statistics on 
which forecasts must be based. It is he who watches 
the trend of past price movements and notes the slight- 
est signs of a change. And it is in his trade journals 
that we find the first discussions of the probable effect of 
gold discoveries or silver legislation on prices and trade. 
The theorist can aid in these predictions only by sup- 
plying or correcting the principles on which they are 
constructed. 



CHAPTER VIII. 

GOLD AND PAPER. 
§1. 

General evidence that an expected cliange in the value 
of money has an effect on the rate of interest can be ob- 
tained from several sources. Municipalities often find 
they can sell gold bonds at better terms than currency 
or coin bonds. The very desire of lenders to insert a 
gold clause in their contracts is strong proof that they 
are willing to yield something for it. This was strik- 
ingly shown in California^ during the war inflation 
period, where for a time, gold contracts could not be en- 
forced and in consequence interest rates were very high. 

During a period of progressive paper inflation it is also 
true that interest is high even when the contract is 
drawn on a paper basis. As we shall see at a later stage, 
this was partially true during the civil war, though its 
effect was not very pronounced owing to the over san- 
guine hopes of an early termination of the war and a 
return to a specie basis. It was also true during the 
currency troubles in the thirties. Raguet wrote : " "In 
the six months before the suspension of ^2>7i although 
the amount of the currency was greater than it had ever 
been before in the United States, yet the scarcity of 
money was so great that it commanded from i^o to 3 ^ 
per month." It would be unsafe to found much infer- 
ence on these facts. Their significance may be partly 

^ Bernard Moses, " Legal Tender Notes in California," Quarterly 
Journal of Economics, October, 1892, p. 15. 

-" Currency and Banking," (1839), p. 139; alsoSumner, " History; of 
Banking," (1896), p. 264. 



38 1] 



Appreciation a7id Interest. 



39 



or wholly different. But they raise a presumption in 
favor of the theory here advanced and against the theory 
that the rate of interest is lowered by inflation of the 
currency. 



A definite test must be sought where two standards 
are simultaneously used. An excellent case of this kind 
is supplied by two kinds of United States bonds, one 
payable in coin and the other in currency. From the 
prices which these bonds fetch in the market it is pos- 
sible to calculate the interest realized to the investor. 
The currency bonds are known as currency sixes and 
mature in 1898 and 1899. The coin bonds selected for 
comparison are the 4^5 of 1907. The following table 
gives the rates of interest realized in the two standards 
together with the premium on gold. 



RATES OF INTEREST REALIZED FROM 


DATES MENTIONED 








TO MATURITy.i 














Price of 














Coin. 


Currency. 








Coin. 


Currency. 






6.4 




Gold. 










Jan., 


1870 . 


5-4 


119. 9 


Jan.. 


1879 • • 


1 3-7 


4-5 


July. 


1870 . 


5-8 


5-1 


112. 2 


Jan., 


1880 . 




i 3-8 


4.0 


Jan , 


187T . 


6.0 


5-3 


I TO 8 


Jan., 


1 881 




• 3-3 


3-4 


July, 


1871 . 


5-8 


50 


113. 2 


Jan., 


1882 




1 3-0 


3-5 


Jan., 


1872 . 


5-3 


4-9 


109.5 


Jan. , 


1SS3 




2.9 


3-3 


July. 


1872 . 


56 


5.0 


113-9 


Jan., 


T884 




\ 2.6 


2.9 


Jan., 


1873 • 


5-7 


5-1 


III. 9 


May, 


1SS5 




1 ^-7 


2.7 


July, 


1S73 • 


5-4 


50 


"5-3 


Jan., 


t886 




1 2.6 


2.6 


Jan., 


1874 • 


5-0 


5-0 


110.3 


Jan., 


1887 




2.3 


2.6 


July, 


1874 . 


50 


4-9 


T10.7 


Mar. 


t888 




2.3 


29 


Jan., 


1875 • 


5-1 


47 


112. 6 


Jan., 


1889 




2.2 


2.6 


July, 


1875 • 


51 


4-4 


1 17.0 


May, 


1S90 




2.T 


2.6 


Jan., 


1876 . 


4-7 


4.4 


112. 9 


July, 


189T 




2.4 


3-0 


July, 


1876 . 


4-5 


4.2 


112.3 


Jan., 


1892 




i '-^ 


3-1 


Jan., 


1S77 . 


45 


4.4 


107.0 


Mar. 


1S93 




i 2.8 


3-1 


July, 


1877 . 


4.4 


4-3 


105.4 


Nov. 


, 1894 




2.7 


3-5 


Jan., 


1878 


50 


4.6 


102.8 


Aug. 


,1895 




2.8 


3-6 


July, 


1878 . 


3.9 


4.4 


TOO. 7 


Aug. 


, 1896 




3.2 


4-3 



^This table has been obtained by the aid of the usual brokers' bond 
tables. In the case of currency bcir.ds, it was only necessary to deduct 
accrued interest (if any) from the quoted price and look in the table 
for the interest which corresponds to the price so found and the num- 



40 American Economic Association. ^ [382 

Several points in this table deserve notice. The quo- 
tations for 1894, '95, '96 show a considerably higher rate 
of interest in the currency standard than in the coin stand- 
ard as well as a higher rate in both standards than in 
previous years. The difference is between 2.7^ and 
3.5^ in 1894, and between 3.2^ and 4.3^ in 1896. 
Both the increase and the wedging apart of the two rates 
are explainable as effects of the free silver proposal and 
its incorporation (July 1896) in the platform of the 
Democratic party. A free silver law v^^ould certainly re- 
duce the value of returns from currency bonds and possi- 
bly also of those from coin bonds. If the mere dread of 
inflation has this effect, it might be supposed that, dur- 
ing the period of actual inflation, the discrimination in 
favor of coin bonds would be even greater. But we find 
the exact opposite to be true. In 1870 the investor 
made 6.4^ in gold but was willing to accept a return of 
only 5.4^ in currency. This fact becomes intelligible 
in the light of the theory which has been explained. It 
meant the hope of resumption. Just because paper was 
so depreciated there was a prospect of a great rise in its 
value. It was not until 1878 when the prospect of a 
further rise disappeared that the relative position of the 
two rates of interest was reversed. After resumption in 
1879 the two remained very nearly equal for several 
years until recent fears of inflation again produced a 
divergence. 

ber of years to maturity. In the case of gold bonds, since the quota- 
tions are given in currency, it is necessary to divide the quoted price 
by the price of gold in order to obtain their price in gold {i. e., 
"coin") and then proceed as above indicated. The quotations of 
prices of bonds and gold are the "opening" prices for the months 
named and are taken from the Financial Reviezv, 1895, the Commer- 
cial and Fitiancial Chronicle, the (New York) Bankers' Magazine 
and the Bankers' Almanac. After 1SS4, January quotations were not 
always available. 



383] AppreciatioJi and Interest. 41 

§3- 

We have found so far that the facts agree with the 
theory previously laid down. But it is necessary further 
to inquire how close is this agreement. For this pur- 
pose, the figures just given are of little value. They 
represent the rates of interest realized for the periods be- 
tween the dates named and the times at which the bonds 
mature. These periods are not the same for the two 
bonds. As has been explained such a rate of interest is 
a sort of average of the rates of interest for the individual 
years of the periods in question. Thus, in the foregoing 
table, the rate of interest in currency opposite January, 
1870, is 5.4^. This is the rate realized between 1870 and 
1899. It is a sort of average of, say, the rate realized be- 
tween 1870 and 1879 and between 1879 and 1899. As 
we shall see the former was 6.3^ and the latter, 4-5/^. 

It is clear that we must seek the rates of interest in 
the two standards for the same periods. In the follow- 
ing table the periods selected terminate on Jan. i, 1879, 
the date of resumption of specie payments. We may 
say, to fix our ideas, that the figures represent the rate of 
interest realized to investors who buy the bonds at the 
dates mentioned and sell them on January i, 1879 ; but 
it is obviously unnecessary to consider the bonds as ac- 
tually either bought or sold, but only as owned. This 
is no nevv^ use of terms. Business men reckon securities 
in their assets at their market prices and if these prices 
rise or fall they count themselves as gainers or losers. 
This gain (or loss) added to the annual interest receipts 
and properly distributed over the time considered gives 
the rate of interest realized. 



42 



American Economic Association. 



[3S4 



RATES OF INTEREST REALIZED FROM DATES MENTIONED TO JAN- 
UARY I, 1879, (Date of Resumption'). 





Coin. 


Currency. 


Appreciation of Currency in Gold. 












Expected. 


Actual. 


j 


i 


a 




January, 1S70. . . q.i 


6.3 


.8 


2.1 


July, 1S70 . . 




6.2 


5-7 


•5 


1.4 


January, 1871 . 




6.7 


63 


•4 


1-3 


July, 1S71 




6.4 


5-7 


• 7 


1.8 


January, 1S72 . 




5-9 


5-7 


.2 


1-3 


July, 1S72 . 




6.2 


5-7 


•5 


2 1 


January, 1873 • 




6.5 


62 


.3 


2.0 


July. i'S73 • ■ 




6.2 


6.0 


.2 


2.8 


January, 1S74. 




5.6 


6 T 


—.5 


2.T 


July. 1874 . . 




5-7 


5-8 




2.4 


Fanuary, 1875 • 




6.0 


5-4 


!6 


3-1 


July, 1875 • . 




6.1 


4.2 


1.8 


4-9 


January, 1876. 




5-4 


41 


1.2 


43 


July, 1876 . . 




5-2 


2.4 


2.7 


4.9 


January, 1877 . 




5-5 


4.0 


1.4 


3-5 


July, 1 87 7 . . 




5.7 


3-1 


2.5 


3.6 


January, 1878. 




8.2 


6.0 


2, 1 


2.8 


July, 1878 . . 




4.8 


2.6 


2,1 


1.4 



' Since the figures in this table represent the rales of interest which 
will render the " present value," at the date of purchase, of all the 
future benefits to January, 1879, equal to the purchase price, they can 
be calculated by Horuer's method as indicated in Chapter V. But the 
method which has been adopted is less laborious, as it ena1)les us to 
use the bond tallies. It can best be explained by an example. The 
opening price, January, 1870, of currency 6's was 109)^, and January, 
1879, ^^9/i, which require no correction for accrued interest. Our 
problem is, if a man spends ^109"/^ in 1870 and receives |ii9>< in 
1879 with $6 per annum (semi-annually) in the meantime, what rate 
of interest does he realize? Now it is clear that the answer is the 
same if all the benefits and sacrifices involyed are doubled or halved 
or increased or decreased in an}' common ratio. Let us then divide 
them all by i.icjyi- Then I91.3 would be paid in 1870 for |;ioo due in 
1879, and ^5.02 per annum in the meantime. That is, the interest 
realized is exactly as if the bond were a 5.02% bond maturing in 1879 
and bought at 91.3 in 1870. This can readily be obtained from the 
bond tables by interpolating between the figures for a 5% and a 5)4% 
bond purchased at 91.3 and having 9 years to run. For a 5% bond 
we obtain 6.28%, and for a 5}4% bond, 6.81%. Hence for a 5.02% 
bond the result is 6,30%, or 6.3%, The third column gives what may 
be called the expected rate of appreciation of currency in terms of 
gold, that is, that rate of appreciation which would have made the 



385] Appreciation and Intej^est. 43 

From this table we see that the interests realized for 
the period, January, 1870 to January, 1879, were, in coin, 
7.1^, and in currency, 6.3%, which, according to the 
formula i + 7 = ( i + z ) ( i + <« ), gives a rate of appre- 
ciation of .8%. This may be called the " expected ap- 
preciation ". The actual rate of appreciation was 2.1%. 
That is, the estimated appreciation was about two-fifths 
of the appreciation as it really turned out. Thus those 
who held currency sixes had the better investment. In 
fact it is w^ell known that many speculators grew rich by 
exchanging gold bonds for currency bonds at this time. 
The table shows the same misjudgment in July, 1870, 
January, 1871, and July, 1871. From then to July, 
1874, the outlook for resumption grew gloomy, due no 
doubt to the strong greenback sentiment. The inflation 
bill of 1874 actually produced a prospect of negative 
appreciation, i, e.^ depreciation. This bill was vetoed by 
President Grant, and in December of that year the bill 
for resumption was passed by the Senate. Accordingly 
January, 1875, opened with a more hopeful estimate. 
The bill became law on the 14th of January and there 
was an immediate rise in the " expected " appreciation 
which, from then on, averaged 2%. But during the 
same period the actual appreciation from the dates named 

two interest rates equally profitable. It is obtained from the formula 
I +y= (i -I- ?■) (i + «)• The last column gives the actual rate of ap- 
preciation between the dates mentioned and January i, 1879. This 
is calculated from the quoted prices of gold. Thus the opening price 
of gold January, 1870, was 119.9, and January, 1879, ^oo- Hence 
currency appreciated in nine years in the ratio 100 to 119.9, which is 
at the race of 2.1% per annum. If the appreciation proceeded uni- 
formly this method would be strictly correct. As it is, a more elabo- 
rate method would be required, in accordance with the principles ex- 
plained in Chapter V, to take account fully of the fluctuations of the 
annual appreciation. But for our present purposes, and for results 
worked out to but one decimal place, the simpler method here 
adopted is sufficiently correct. 



44 American Econoviic Association. [386 

to January, 1S79, averaged 3.6%, so that even after the 
government promised resumption, investors and specula- 
tors did not put implicit confidence in that promise, the 
"expected" appreciation being only a little more than 
half the actual appreciation. This corresponds to the 
well known fact that the resumption act was then looked 
upon as a political manoeuvre, likely to be repealed. 



It should be observed that the method employed to 
determine the rate of interest realized is open to oiie 
danger. It correctly represents the rate of interest act- 
ually realized between tw^o dates, but, unless the later of 
the two dates is maturity, it does not necessarily repre- 
sent the rate of interest expected at the first date. The 
investor could not know in January, 1870, what the price 
of bonds would be in January, 1879, unless the bonds 
matured at that time. To compare, in 1870, the relative 
advantages of coin and currency bonds for the period 
1870-79, a forecast was necessary, not only of the rela- 
tion of currency to gold, but also of the prices of the two 
bonds in 1879. These prices in turn depend on a new 
forecast made in 1879. It follows that a mistake in this 
forecast of 1879 ^^^ embodied in the prices of that year 
wall affect the rate of interest realized between 1870 and 
1879 in the same manner as a mistake of the opposite 
kind in the forecast of 1870. 

But in most cases the method given is sufficiently 
exact. For, although in 1870 it would have been im- 
possible to predict exactly the prices of the two bonds in 
1879, yet it can usually be depended upon that any great 
change in price is apt to affect both alike (provided they 
have approximately the same time to run) and thus 



387] Appreciation and Interest. 



45 



eliminates itself for the most part in the comparison. 
For this reason it is clearly better to take bonds whose 
dates of maturity approximately correspond, in order 
that any abnormal influence in 1879 may affect both 
alike, than to take, for instance, currency sixes of 1899 
and coin bonds of 1881. 



48 American Economic Association. [390 

From this table it will be seen that the rates realized 
to investors in bonds of the two standards differed but 
slightly until 1875, when the fall of Indian exchange 
began. The average difference before 1875 was .2^ 
while the average difference since 1875 has been .7^, 
or more than three times as much. 

From 1884 exchange fell much more rapidly than be- 
fore, and the difference in the two rates of interest rose 
accordingly, amounting in one year to i.i^. Since 
the two bonds were issued hy the same government, 
possess the same degree of security, are quoted side by 
side in the same market and are in fact similar in all 
important respects except in the standard in which the}- 
are expressed, the results afford substantial proof that 
the fall of exchange (after it once began) was discounted 
in advance. Of course investors did not form perfectly 
definite estimates of the future fall, but the fear of a fall 
predominated in varying degrees over the hope of a rise. 

The year 1890 was one of great disturbance in ex- 
changes, the average for the first six months being 17.6 
and for the last six months 19.3. The gold price of 
the silver bonds rose from an average for the first six 
months of 73.8 to 83.5 for the last six months, but the 
rise in their silver price was only from 100.6 to 103.7, 
showing that the increase of confidence in the " future 
of silver" was not great and in fact only reduced the 
disparity in the interest from i.o to .8^. 

This great rise in exchange and the slight revival in 
silver securities occurred simultaneously with the pas- 
sage of the Sherman act of July, 1890, by which the 
United States was to purchase four and a half million 
ounces of silver per month. There can be little doubt 
that the disturbance was due in some measure to the 
operation or expected operation of that law. 



39 1] Appreciation and Interest. 49 

This is not the only case in which the relative prices of 
rupee paper and gold bonds were probably affected by po- 
litical action. The smallest difference (since 1874) in 
the tw^o rates of interest occurs in 1878, which was the year 
of the Bland act and the first international monetary 
conference. 

After the closure of the Indian mints on June 26, 1893, 
exchange rose from 14.7 to 15.9, the gold price of rupee 
paper from 62 to 70 and consequently its rupee price 
from 101.2 to 105.7. 

§ 2. 

The preceding comparisons serve to establish the in- 
fluence of the divergence between the standards on the 
rates of interest, but afford no measure of that influence. 
The rates of interest which have been deduced for gold 
bonds were the rates realized if the bonds were held to 
maturity. The rupee bond had no fixed date of matur- 
ity and had to be treated as a perpetual annuity, although 
it differed from such an annuity in being terminable by 
the government at par on three months' notice. 

In order to measure the extent to which the fall of silr 
ver was allowed for by investors, it is necessary to exam- 
ine the rates realized during specified periods. The fol- 
lowing table gives the rates realized between the first 
five and the last five years of the period of falling ex- 
change. 



50 



American Economic Associatioii. 



[392 



RATES OF INTEREST REALIZED ON INDIA BONDS FOR PERIODS 
SPECIFIED.! 





Silver. 

. 
J 


Gold. 

i 


Appreciation of Gold in 
Silver. 




Estimated. 
a 


Actual. 


1875-91 .... 

1876-92 .... 

1877-93 .... 
1878-94 .... 
1879-95 .... 


4.1 
4.3 

4-5 
4.6 
4.8 


3-5 
3-6 
3-6 
3.8 
3-9 


.6 

.7 
•9 
.8 
•9 


1.6 
1.8 
2.1 
2.6 
2.4 


Average .... 


4-5 


3-7 


.8 


2.1 



The average estimated appreciation for the periods 
taken is .8%, which is slightly more than one third of 
the average actual appreciation, 2.1%. Perhaps to ob- 
tain the net estimate of investors as to the fall of ex- 
change we ought to deduct from the .8% another .\^'/o due 
to the trouble and expense of obtaining English money 
for Indian exchange, for it will be remembered that even 
before the fall of exchange began, the rates yielded to 
investors differed by .2%.^ We thus obtain ,7% as the 
extent to which, on the average, investors protected 
themselves against the fall in silver during the period 

' The methods by which the first columu is computed are the same 
as those explained in the preceding chapter, account being taken of 
the fact that the price quotations for rupee paper are not "flat," so that 
no corrections for accrued interest need be applied. For computing 
the second column a more laborious method was necessary, due to the 
fact that the quotations are not continuous for the same bond. The 
earlier ones are for a 4 % bond and the later for a 3 % bond. The 
buyer of a 4 % bond is regarded as converting it into the 3 % at the 
current price in 1888, the date of maturity of the earlier bond. As no 
bond tables apply to such conversions, tables of present values were 
used and that rate was found by trial (and interpolation) which would 
make the present value of all benefits equal to the purchase price. 

^This probably included besides the brokerage and trouble of ob- 
taining and selling " interest bills ", the risks even at those early 
dates of a falling or fluctuating exchange. 



393] Appreciation and hiterest. 51 

named. The remaining fall, 1.4%, implies a rela- 
ative loss to the holders of rupee paper and a gain 
to the holders of gold bonds. Had the business 
world fully foreseen the fall of Indian exchange, rupee 
paper would have been cheaper or gold bonds dearer 
than they actually were, or both. The rates of interest 
realized in the two standards during the periods men- 
tioned would have been spread apart ( at most ) i ^/^ ^ 
further. 

§3. 

The question arises at this point, how is this 1)4 fo to 
be distributed? Did investors overestimate silver or 
underestimate gold most ? There is nothing in the fore- 
going investigation to decide this vexed question. Our 
quantitative result is purely a differential one. But 
other sorts of evidence point strongly to the conclusion 
that the major part of the miscalculation was on the sil- 
ver side. So far as " demonetization " is concerned, the 
effect on silver must have been, according to any reason- 
able view, greater than the effect on gold, and in conse- 
quence any unforeseen part of these effects would be 
probably greater in the case of silver than in the case of 
gold. So far as production is concerned, the disturb- 
ance in silver was far greater than that in gold either 
when reckoned absolutely or in proportion to the total 
masses whose values would be affected. Finally, since 
the break-down of bimetallism in 1873-4, the world-wide 
agitation to " rehabilitate silver " has held out a delusive 
hope which must have acted to give the silver bonds a 
higher price than they " were worth." The strength of 
this agitation need scarcely be dwelt on here. It found 
expression in many bills in Congress which were never 
passed and in two which were passed, in numerous pro- 



50 



American Economic Association. 



[39- 



RATES OF INTEREST REALIZED ON INDIA BONDS FOR PERIODS 
SPECIFIED. 1 





Silver. 


Gold. 


Appreciation of Gold in 
Silver. 




Estimated. 


Actual. 




J 


z 


a 




1875-91 .... 

1876-92 .... 

1877-93 • . . . 


4.1 
4.3 
4-5 


3-5 
3-6 
3.6 


.6 

• 7 
•9 


1.6 
1.8 
2.1 


IS78-94 .... 


4.6 


3.8 


.8 


2.6 


1879-95 .... 


4.8 


3-9 


•9 


2.4 


Average .... 


4-5 


3-7 


.8 


2.1 



The average estimate4 appreciation for the periods 
taken is .8%, which is slightly more than one third of 
the average actual appreciation, 2.1%. Perhaps to ob- 
tain the net estimate of investors as to the fall of ex- 
change we ought to deduct from the .8% another , i % due 
to the trouble and expense of obtaining English money 
for Indian exchange, for it will be remembered that even 
before the fall of exchange began, the rates yielded to 
investors differed by .2%.^ We thus obtain .7% as the 
extent to which, on the average, investors protected 
themselves against the fall in silver during the period 

^ The methods by which the first column is computed are the same 
as those explained in the preceding chapter, account being taken of 
the fact that the price quotations for rupee paper are not "flat," so that 
no corrections for accrued interest need be applied. For computing 
the second column a more laborious method was necessary, due to the 
fact that the quotations are not continuous for the same bond. The 
earlier ones are for a 4 % bond and the later for a 3 % bond. The 
buyer of a 4 % bond is regarded as converting it into the 3 % at the 
current price in j8S8, the date of maturity of the earlier bond. As no 
bond tables apply to such conversions, tables of present values were 
used and that rate was found b}' trial (and interpolation) which would 
make the present value of all benefits equal to the purchase price. 

^This probably included besides the brokerage and trouble of ob- 
taining and selling " interest bills ", the risks even at those early 
dates of a falling or fluctuating exchange. 



393] Appreciation and Interest. 51 

named. The remaining fall, 1.4%, implies a rela- 
ative loss to the holders of rupee paper and a gain 
to the holders of gold bonds. Had the business 
world fully foreseen the fall of Indian exchange, rupee 
paper would have been cheaper or gold bonds dearer 
than they actually were, or both. The rates of interest 
realized in the two standards during the periods men- 
tioned would have been spread apart ( at most ) i ^^ ^ 
further. 

§3- 

The question arises at this point, how is this i}4 fo to 
be distributed? Did investors overestimate silver or 
underestimate gold most ? There is nothing in the fore- 
going investigation to decide this vexed question. Our 
quantitative result is purely a differential one. But 
other sorts of evidence point ^t^ongly to the conclusion 
that the major part of the miscalculation was on the sil- 
ver side. So far as " demonetization " is concerned, the 
effect on silver must have been, according to any reason- 
able view, greater than the effect on gold, and in conse- 
quence any unforeseen part of these effects would be 
probably greater in the case of silver than in the case of 
gold. So far as production is concerned, the disturb- 
ance in silver was far greater than that in gold either 
when reckoned absolutely or in proportion to the total 
masses whose values would be affected. Finally, since 
the break-down of bimetallism in 1873-4, the world-wide 
agitation to " rehabilitate silver " has held out a delusive 
hope which must have acted to give the silver bonds a 
higher price than they " were worth." The strength of 
this agitation need scarcely be dwelt on here. It found 
expression in many bills in Congress which were never 
passed and in two which were passed, in numerous pro- 



52 American Economic Association. [394 

posals in Germany, in silver commissions there and in 
England, and in three international conferences. If any 
further evidence is needed that this agitation contrib- 
uted to mislead investors as to the future of silver, it 
can be found by examining the discussions and mistaken 
prophecies on silver, contributed to the Economist and 
other trade journals. It would seem extremely improb- 
able that these hopes for the " rehabilitation of silver " 
have acted to depress the price of gold bonds rather than 
to raise the price of silver bonds. 

For these reasons it seems likely that, of the lyi'fo 
relative gain or loss, not more than half represents an 
unexpected gain on the gold bonds. That is, the inter- 
est realized on the gold bonds, if higher than it should 
be, was not higher by more than Y^'fc If this be true 
of one gold investment it was undoubtedly true of all 
gold investments and of the whole money market in 
London. This affords therefore, a probable upper limit 
to the debtor's loss in England for contracts made since 
1874. But even if the miscalculation was twice as great 
for gold as for silver, the upper limit becomes only i ^. 

Our result therefore, is that the average debtor's loss 
in London for contracts made since the fall of silver be- 
gan, was probably less than y^ ^ and almost certainly 
less than i ^ per annum. In Chapter X we shall at- 
tempt to find a lower limit. 



A great deal has been written on the loss incurred by 
India in paying her annual interest to England in gold, 
but little is said of the interest paid at home in silver. Of 
India's national debt, about ^100,000,000 are in gold 
and Rx 100,000,000 in rupees. This rupee debt was 



395] Appreciation and Interest. 53 

almost all in force twenty years ago and was then equiva- 
lent to ^100,000,000, but today it is worth only ^60,- 
000,000. The difference may mean an added burden of 
gold debt, but it may also mean a lessened burden of 
silver debt and it is by no means impossible that, so far 
as national indebtedness is concerned, India is better off 
than she would, have been if a bimetallic tie between 
silver and gold had been maintained. 

In this connection it may be worth while to point out 
a curious oversight in Mr. Elijah Helm's recent book.^ 
In Chapter XVI he proposes the conversion of the 4^ 
rupee debt into a 3^ gold debt and, assuming very 
plausibly that the gold bonds could be sold for 99, shows 
that so long as exchange remained at its present level, 
there would be an annual saving of interest oi Rs 
160,000. This is correct enough, but he next attempts 
to show that if exchange should gradually fall there 
would continue to be a saving until it should sink to 
ioj4d. This is entirely erroneous. It takes account only 
of the annual interest and not of the deferred principal 
which if in gold, grows progressively onerous in terms 
of silver. It is odd that a bimetallist who portrays so 
vividly the evils to the debtor from an appreciating gold 
principal should have found himself in the position of 
deliberately advising a debtor to adopt that standard to 
lessen his burden of interest. In the same year that 
Mr. Helm's book was written, the Indian Government 
converted its 4^ rupee debt, not into gold, but into 
another rupee debt at S}4 fo. 

1 "The Joint Standard," (London and New York, 1894.) 



CHAPTER X. 

MONEY AND COMMODITIES. 

§1. 

In attempting to apply our theory to periods of rising 
and falling prices, we are met by the difficulty that 
comparison can only be made between successive periods. 
We can learn what the rate of interest has been since 
1873, ^^^ "^^ cannot know what it would have been if 
bimetallism had been extended or if the world's cur- 
rency had been so expanded as to have prevented the 
fall of prices. Without this missing term of compari- 
son, it is difficult to measure the influence of the pro- 
gressive scarcity of gold, if such there has been, upon 
the rate of interest. It does not answer the purpose 
merely to compare the rates of interest before and after 
1873. No two periods are so alike industrially that we 
can say they differ only in the state of the monetary 
standard. Other influences innumerable affect the 
" value of money" on the money market. Individual 
quotations at different times on the same market vary 
from one half of one per cent, to fifty per cent, while 
yearly averages vary from one to seven per cent. We 
can never wholly eliminate all causes but one, and even 
partial elimination is possible only by taking averages 
for periods of several years each. In spite of these diffi- 
culties however, certain general conclusions can be 
established. 

§2. 

Our main problem is not concerned with high and 
low prices but with rising or falling prices. But we 



397] 



Appreciation and Interest. 



55 



note in passing an important generalization in regard to 
price levels and the rate of interest. Shall we associate 
high interest with high prices or with low prices ? To 
answer this question the following table is constructed. 
Two rates of interest are given for each decade. The 

MARKET RATES OF INTEREST IX RELATION TO HIGH 
AND LOW PRICES.i 



1824 to 

: 1831 

; incl. 


1832 to 1842 to 
1841 1851 
incl. incl. 


1852 to 

I86I 

incL 


1862 to 
1871 
incl. 


1872 to 
1881 
incl. 


1882 to 
1891 
incl. 


London, High prices 
" Low prices . 


13.8 
; T, 2 


4.4 3-6 
3.2 2.6 


5-4 
3-0 


5-1 

2.6 


3-7 

2.5 


30 
2.5 


New York, High prices . . 
" Low prices .... 




9-1 
91 


7.4 
6.7 


7.0 

5-1 


5-3 
5.1 


Berlin, High prices 
" Low prices . 






4.6 

3-4 


3-7 

3-2 


3-3 
2.7 






Paris, High prices . . . 
" Low prices .... 


i 




4.1 
2.4 


2.6 
2.6 


^ Calcutta, High prices 
" Low prices . 






6,2 
5-6 


5-4 
6.2 






' Tokyo, High prices . . 
" Low prices .... 






■ 


12.3 
12.0 


lO.I 

10. 1 


* Shanghai, High prices 
" Low prices . 




' i 




; 6.0 




. . ; . . ! . . 1 . . 




i 5-7 



^ This table is constructed from the data given in the Appendix. 
For New York, the rates for the first decade are averaged from the 
column in the Appendix headed "60 days," and are not to be com- 
pared with those for the remaining decades, which are averaged from 
the column headed " Prime two name 60 days." The index numbers 
of prices which have been employed are those of Jevons (1S24-51) 
and Sauerbeck (1S52-91) for England, Soetbeer and Heinz for Ger- 
many, the Aldrich Senate report for the United States and France, 
and the Japanese report for India, Japan and China. (See Appendix, 
\ 3). The table ends in 1S91 because there are no index numbers for 
the United States since that year. 

2 For Calcutta the rate for the bank of Bengal is employed, no 
"market" rate being available. The first column is for 1873-81 in- 
stead of 1S72-81, for the reason that no index number for 1872 is 
available. 

* For Tokyo the first column is for 1S73-81 for the same reason. 

* For Shanghai the period is 1S85-93 instead of 1S82-91, for the rea- 
son that the available rates begin in 1885 and the index numbers end 
in 1893. 



56 American Economic Associatio7i. [398 

first, opposite " high prices," is the average rate for 
those years of the decade whose price levels, as shown 
by an index number, were above the average price level 
for the whole decade ; the second is the average rate for 
the years whose prices were below the general average. 

Of the 21 comparisons contained in this table, 17 show 
higher rates for high-price years than for low-price 
years, one shows the opposite condition and three show 
equal rates in the two cases. As the table covers 68 
years for London, 40 for New York, 30 for Berlin, 20 
for Paris, 19 each for Calcutta and Tokyo, and 9 for 
Shanghai, or 205 years in the aggregate, the result 
may be accepted with great confidence that high and 
low prices are usually associated with high and low 
interest respectively. 

There are two probable reasons for this connection. 
One is that high general prices usually mean scarcity of 
capital rather than abundance of money, while low prices 
generally mean abundance of capital, not scarcity of 
money. This corresponds to the observations of Jevons 
on the relation of the rate of discount to the price of 
wheat ; ^ the other reason is connected with periods of 
speculation and depression and will be discussed in § 12. 

§3. 

The relation of high or low |)rices to the rate of inter- 
est must not be confused with the relation of rising or 
falling prices to the rate of interest ", to which vv e now 
turn. 

^ "Investigations in Currency and Finance," (1884), p. XIV. 

^ de Haas appears to have fallen into this confusion both in his crit- 
icism of Jevons and in his treatment of statistics. See "A third 
element in the rate of interest," Journal of the Royal Statistical 
Society, March, 1889. 



399] Appreciation and Interest. 57 

It was predicted by Mr. Gibbs/ formerly a director of 
the Bank of England, and by other eminent bimetallists 
that the progressive scarcity of gold would raise the rate 
of interest. Such a scarcity makes a stringency in the 
money market, and the banks, each struggling to attract 
reserves from the others, will raise their rates. This 
prophecy, however, has not been fulfilled. Scarcely had 
Mr. Gibbs made his prediction when the rate fell enor- 
mously. Some monometallists have argued from this fact 
that there has been no appreciation of gold ^. But the 
theory that appreciation raises interest has been confi- 
dently afiirmed on both sides and has even received the 
stamp of approval of Mr. Giffen.^ It is, however, utterly 

' "The Bimetallic Controversy," (London, 18S6), pp. 19, 231, 245-8-9, 

373- 

2 Report of the Gold and Silver Commission, (1888), p. 120; also 
Professor Laughlin in Quarterly Journal of Economics, Vol. i., p. 344. 

3 " Essays in Finance," (2d series, 1886), p. 70. " The years oi fall- 
ing prices and rising prices also correspond as a rule with those years 
in which high rates and low reserves, and low rates and high reserves 
are combined." This (so far as prices and interest are concerned) is 
not only the exact opposite of the truth but it is flatly contradicted by 
the few figures which Mr. Giflfen himself brings forward. Of these 
he says : " . . in years like 1865 and 1866 with which the Table 
begins, there is an obvious connection between the low reserve and 
high rate of discount of those years and the high Index No., leading 
in the following [!] years 1867-71 to a simultaneous fall in the Index 
No. and the rates of discount . . " He adds : " . . the low 
prices rather succeed the high discount rates than exactly correspond 
. . " Coming to the recent period of gold contraction, he says : 
" Turning to the rate of discount, we find the facts once more in cor- 
respondence. What we find first is a striking disturbance of the 
money market at the maximum period of high prices, 1871-73 [a pe- 
riod of rising prices and high interest], when the contraction of gold 
begins." Of the period 1875-79 (falling prices and low interest), he 
writes: "With a minimum average monthly rate of 2 per cent in 
each year, the following maximum monthly rates were nevertheless 
touched, viz" : [4^, 4f, 4f, sf, 4^ %s]. "In the present year (1885) 
when with dull trade and low prices the reserve should be full and 
discount rates low, we find that with a minimum of 2 per cent, there 
is again to be a comparatively high maximum (4 %) within the year." 



58 American Ecoyiornic Associatio7i. [400 

at variance with facts. Tliat an abnormally high or low 
bank reserve is correlated with low and high interest is 
abnndantly justified in theory and verified in practice.' 
But the normal bank reserve itself shrinks with a 
shrinkage of gold and in consequence the inference that a 
contraction of the general gold supply will raise interest 
is fallacious.^ 

When prices are rising or falling, money is depreciat- 
ing or appreciating relatively to commodities. Our 
theory would therefore require high or low interest ac- 
cording as prices are rising or falling, provided we as- 
sume that the rate of interest in the commodity stand- 
ard should not vary. This assumption would be thor- 
oughly justified only in case the two periods were eco- 
nomically alike in all respects except in the expansion 
or contraction of credit and currency. In the following 

"To sum up — what I have to say of the recent discount rates is that 
while there has been an undoubted fall in recent years, corresponding 
to the abundance of capital, yet the market has been fevered by the 
demands on the reserve . . " "The monetary history of recent 
years has accordingly been very like what was to be expected on the 
theory above set forth, assuming a contraction of gold to have oc- 
curred, . . finally the money market has been irritable and fever- 
ish in a remarkable manner during the period of contraction." Thus, 
beginning with a statement that years of falling and rising prices cor- 
respond to years of high and low interest, Mr. Giffen cites facts which 
show that the opposite is true, but proceeds complacently to compare 
the rates of periods of rising (or falling) prices with the prices of the 
succeeding period of falling (or rising) prices. As the period of fall- 
ing prices in which he writes is unfinished, he can onl}- say of it that 
the "money market has been irritable and feverish in a remarkable 
manner." Another monometallist, Clarmont Daniell, objects to bi- 
metallism for India on the ground that it would deplete India of silver 
and raise the rate of interest. ( "The Bimetallic Controversy," p. 257). 
On this point see \ 5. 

^See, ^. ^., Giffen's "Essays," ibid., or the diagrams in Clare's 
" Money-Market Primer," L,ondon, 1891 ; also F. M. Taylor, "Do we 
want an Elastic Currency," Political Science Quarterly, March, 1S96, 
pp. 133-157- 

^ See, however, § 12, note. 



40i] 



Appreciation and Interest. 



59 



table for London the periods are selected to correspond 
with the main movements of prices. Thus the period 
1826-29 was a period of falling prices so that money ap- 
preciated in terms of commodities at the average rate of 
\.2fo per annum. This is indicated in the third column 
by the figure +4.2. In the period 1836-39 prices rose 
so that money fell at the rate of 2.3^ per annum, indi- 
cated by — 2.3. 

I^ONDON RATES OF INTEREST IN REIyATlON TO RISING 
AND FAI,I,ING PRICES.i 









Appreciation of 


virtual Interest 




Bank. 


Market. 
i 


Money in 
Commodities, 

a 


m 
Commodities. 

(Market.) 
J 


1826 — 29 • • 


4.4 


3-5 


4-4.2 


7.8 


1830—35 






4.0 


3-2 


0.0 


3-2 


1836—39 






4-7 


4.2 


—2.3 


1.8 


1840—44 






4.2 


3-5 


+5.9 


9.6 


1845—47 






3-7 


4.2 


— 3-0 


I.I 


1848—52 






2.9 


2-5 


+ 1.2 


37 


1853—57 






4.1 


5-3 


—2.4 


2.8 


1858—64 






4.4 


4.2 


— 3-0 


I.I 


1865—70 






3-8 


3.6 


+ 1.1 


4-7 


1871—73 






3-9 


3-7 


—6.2 


—2.7 


1874—79 






3.2 


2.7 


-f4-3 


7-1 


1880—87 






3-3 


2.6 


+3-8 


6.5 


1888—90 






3-8 


2.9 


—1.4 


1-5 


1891—95 




2.6 


1.6 


+3.8 


5-5 


Mean Variation, 


•5 


■ 7 




2.6 



^ This table is constructed from the data in the Appendix. The 
third column is based on index numbers, (Jevons' for 1826-52, and 
Sauerbeck's for the remaining years). The index numbers for two 
dates, as 1826 and 1829, being given, their inverse ratio gives the rela- 
tive value of money (in commodities), at those two dates. From these 
it is easy to calculate the average annual change in its value. Theo- 
retically, since the loans here included run usually, perhaps 30 to 90 
days, the quotations averaged should begin at the first of the two dates, 
and cease, say, 60 days before the second. But the index numbers are 
not always for definite points of time, nor can the interest quotations 
be subjected to such minute corrections without an immense expendi- 
ture of labor. Hence, the method adopted has been to average the 
rates for all the years of a period, e.g., for the four years, 1S26-29, 
while the "appreciation" is reckoned between those dates, and 
thus is an average for only three years. If the index numbers repre- 



6o American Economic Association. [402 

If this table be exaiiiiiied in successive periods, it will 
be found, in eleven out of thirteen sequences for bank 
rates and in ten out of thirteen for market rates, that in- 
terest is high or low according to the degree in which 
prices are rising or falling. Attention is called particu- 
larly to the period 1S53-57 during which prices rose 
very fast simultaneously with and presumably because 
of the great gold production. The market rate of in- 
terest averaged 5.3/^ which was far higher, not only 
than in any subsequent, but also than in any previous 
period, although it can scarcely be supposed that capital 
was less abundant This fact has been commented upon 
by various writers, ^ and is usually attributed to trade ac- 
tivity and speculation. Such a reason, however, is not 
really explanatory unless the reason for the speculation 
is also given. 

The theory here offerred, that the high rate represent- 
ed an effort to offset the depreciation of money, not only 
affords a complete explanation but in connection with 
another fact soon to be noted, explains the trade activ- 
ity also. 

§4- 

The following table for Berlin displays the same con- 
nection between price movements and interest. 

sent the price levels at the middle of 1826 and of 1829, then the average 
interest rates ought in theory to include only the last six months of 
1826, and the first four months of 1829. But it seems better to include 
too much at both ends, than to omit the averages for 1826 and 1829 
altogether, for the reason that an average is the more valuable the 
greater the number of terms included. The method adopted also 
seems better than omitting either otie of the extreme years, partly for 
the reason just given, and partly because both years usually belong 
to the same economic movement. 

^ E.g., Sir Louis Mallet. Note to Report of Gold and Silver Com- 
mission, ( 1888) p. 120; andjevons' " Investigations in Currency and 
Finance," (1884) p. 95. The latter will be again referred to. 



403] 



Appreciation and Interest. 



61 



BERLIN RATES OF INTEREST IN REI.ATION TO RISING 
AND FALLING PRICES. 1 



Bank. 



Market 



Apprecia- 
tion of 
Money in 
Commod- 
ities. 
a 



Virtural 
Interest in 
Commod- 
ities. 
(Bank.) 
h 



Virtual 
Interest in 
Commod- 
ities. 
(Market.) 

J2 



1851-52 

1853-57 ■ 

1858-64, 

1865-70 

1871-73 

1874-79 

1880-83 

1884-88 

1889-91 

1892-95 



4.0 
4-7 
4-3 
4-7 
4-5 
4-3 
43 
3-6 
4.0 
3-4 



3-7' 

4.0 

4.1 

3-2 

3-4 

2.5 

3-1 

2.2 



-1-5 

-3-3 

— 2.2 

0.0 

-4 I 

+3.I 
—0.1 
+2.9 
—1.4 
+5-2 



2.4 
1.2 
2.0 



1.4 
4.0 
—0.2 
6.4 
3-3 
5-5 
1-7 
7-5 



Mean variation, 1858-91 



• 4 



2.1 



In the foregoing table the relation is observed in six 
out of nine sequences for bank rates (one being neutral) 
and in six out of seven for market rates. 

For France, index numbers covering a wide range of 
articles are not available. Using those given in the Al- 
drich report for sixteen articles, we have : 

PARIS RATES OF INTEREST IN RELATION TO RISING 
AND FALLING PRICES. 2 



1861-64. 
1865-70 . 
1871-73. 

1874-79 . 
1880-86. 
1887-90. 
1891-95 , 



Bank. 



5-1 
3-2 
5-3 
3-1 
3-2 

3-1 
2.6 



46^ 

2.6 

2.8 
2.6 
2.0 



Appreciation in 
Commodities. 



+ 3-6 

- 4.5 
+ 43 
+ 2.3 

— 5-1 



1 This table is constructed from the data in the Appendix. The 
average in the second column, marked (i), is for the years 1861-64, 
not 1858-64. The "appreciation" is calculated from the figures of 
Soetbeer and Heinz, as given in the Aldrich report. 

2 This table is constructed from the data in the Appendix. The 
average in the second column marked (2) is for the years 1872-73, not 
1871-73. 



62 



A?}!C7'ica?i Economic Association. 



[404 



Here the law is observed in five out of six sequences 
for bank rates and three out of four for market rates/ 

It will be noted that the course of prices and interest 
has been very similar in England, Germany and France. 

For New York we have the following table : 

NEW YORK RATES OF INTEREST IN RELATION TO RISING AND 
FAI^IvING PRICES AND WAGES.2 











i 


0-° 


I.S 




in 

1-1 — 


0] 








g-0 


a C-I3 


^ 


ii'-S" 


i!^? 


OJ ,U! 


ii.. (J 






60 


gv§ 


•■3 >.2 


rt 


CO:? 


.9 2 a 


•i^.§i^' 


s a 




Call. 


days 




< u 




s a 




15^ 


3'-'— 






t 


I 


a 


a 


J 


-7 


> 


y 


1849-57 • . 


6.2 


9.2 




-3-8 


-I.I 


5-1 




8.0 




1858-60 . . 


5.0 


7-4 




+b.4 


— I.O 


14-3 




b-z 




1861-65 . . 


5-9 


8.4 


6.8 


—20.2 


-9-3 


-13-5 


— I4.S 


-1.7 


—3-1 


1866-74 . . 


5-4 


8.4 


7-5 


-h4.7 


-05 


13-5 


12.6 


7-9 


7.0 


1875-79 • • 


. . 




5-1 


+7.9 


4-3-2 




13-4 




85 


1880-84 • • 






5-4 


+0.6 


—2.0 




6.0 




3-3 


1885-91 . . 






5-1 


— 2 


-1-3 




4-9 




3-7 


1892-95 . . 






4.6 






. 








Mean varia- 




















tion, '66-91 






.6 








3-8 




2.1 



We find here the same association of appreciation and 
interest in all of the three sequences for call loans, in 
two of the three cases for 60 days paper (the third being 
neutral) and in three of the five cases for " prime " paper.^ 
This is with reference to commodities. The same holds 
true in reference to wages. We find in the successive 
periods that interest is high or low according to the degree 
in which wages rise or fall. This is true in each of the 
three sequences for call loans, in two of the three for 60 
days paper and in three of the four, for " prime " paper. 

^Assuming that prices fell, 1891-95. 

'^ This table is constructed from the data in the Appendix. The 
rates of appreciation are calculated from Falkner's figures for prices 
and wages in the Aldrich Report. 

3 Assuming that prices fell, 1892-95. 



405] Appreciatio7i and Interest. 63 

Perhaps the most remarkable fact in this table is 
the extremely low rate for 1875-79. '^he average 
is 5. 1 /^ which is the next but lowest in the table, 
the lowest being 4.6% for 1892-95. The extra- 
ordinary change in interest rates beginning in 1875 
has been observed before ; but its connection with the 
resumption act (as it seems to the writer) has been mis- 
construed, Thus William Brough referring to that act 
says : ^ " The mere announcement of our intention to 
put our money on a sound metallic basis had brought 
capital to us in such abundance that the resumption was 
not only made easy, but the normal rate of interest was 
reduced. . . . This remarkable reduction . . is ex- 
plainable only on the ground of a large influx of foreign 
capital." But this explanation would naturally require 
a still lower rate of interest after resumption had been 
accomplished. As the facts are the opposite, there 
seems little room for doubt that the rate of interest was 
simply accommodating itself in some degree to the rapid 
appreciation involved in a return to specie payments. 

§5- 

The preceding statistics apply to gold standard 
countries. Index numbers for silver standard countries 
are not available prior to 1873. It is, however, a priori 
probable that the relative price movements in gold and 
silver standard countries before and after the rupture of 
the bimetallic tie in 1874 presented a strong antithesis. 
This event marked a change in gold standard countries 
from rising to falling prices, while in silver standard 
countries prices began to rise. Unless, therefore, prices 
in silver countries had been rising previous to 1874, and 

1 " Natural Law of Mouey," (New York, 1894), p. 124. 



64 



American Economic Associatio7i. 



[406 



rising very fast indeed, the antithesis referred to must 
have existed. It is, consequently, of much interest to 
inquire whether the fall in the rate of interest which 
was so marked for gold countries was shared in equal 
degree by silver countries. The following table for 
periods of five years before and after the silver and gold 
standards began to diverge, throws some light on this 
problem. 

AVERAGE BANK RATES IN GOI^D AND SILVER STANDARD COUNTRIES 
BEFORE AND AFTER THE BREAKDOWN OF BIMETAI^USM.! 



















^ 


Tl 


















W u) 





















u^ 























iH tn 
















a 


"" t! 




















a 






3 






a 


a 



.9" 


_«■ 





lU 3 
MO 


11 i! 

^5 









fi, 





u 


cd 




> u 




tJ 


fi 


m 


hT 


m 


&< 


% 


< -^ 


< 


1870-74. . 


5-1 


16.4 


10.6 


3-7 


4-5 


4.9 


7-5 


10.7 


5-2 


1875-79- • 


b.5 


14.6 


9.2 


3-0 


4.2 


2.9 


5-1 


10. 1 


3-y 



While the results are not conclusive, they go to con- 
firm our theory. In all gold countries the rate fell 
after the par of exchange with silver countries was 
broken, while in India it rose, and this in spite of the 
flow of capital to India from England and other gold 
countries. It is true that in Japan and China the rates 
fell. But this fall was much less than in the gold 
countries, whereas we should expect it to be much greater 
if the only influence at work were the migration of 

^Tbis table is constructed from the data given in the Appendix. 
Bank rates are selected rather than market rates, as the latter are not 
available for Calcutta and Shanghai. For New York, however, the 
rates for " prime two name 60 days paper " are employed. Although 
the United States and Japan were on a paper basis at the periods 
given, the premium on gold in the one case and silver in the other 
moved in opposite directions, affording, therefore, as great or greater 
antithesis than if the standards had been simply gold and silver. For 
the American premium see Chapter VIII, § 2 ; for the Japanese, see 
Appendix, \ 3, note. 



407] 



Appreciation and Interest. 



65 



capital. Such extraordinary rates as ruled in China and 
Japan in the '70's must have been extremely sensitive to 
the influence of an influx of capital. Even though 
British investment in Japan or China may have been 
much less than in India, we should expect its tendency 
to reduce the native rate of interest to be more effective 
where that rate was 10^ or 15 ^ than where it was 5 ^. 
An added reason for a fall in rates in Shanghai and 
Tokyo is the narrowness of the areas affected by foreign 
capital, which, having little opportunity to penetrate 
inland, tends to glut the market in the open ports. 

Turning to the period for which index numbers are 
available, we have the following table for India, Japan 
and China. 

RATBS OF INT:EREST IN R^I/ATION TO RISING AND FAI^LING PRICES 
IN CAI,CUTTA, TOKYO AND SHANGHAI.i 





Bank. 


Market. 


Appreciation in 
Commodities. 


Calcutta .... 


1873-75 
1876-78 
1879-85 
1886-89 
1890-93 


5-3 
6.8 

5-9 
6.0 

4-3 




+2.6 
— II.O 

+3-8 
-2.6 

-4-7 


Tokyo 


1873-77 
1878-81 
1882-86 
1887-93 


14.0 
16.3 
12.8 

9-3 


12.0 
12.2 
10.3 

9-4 


—0.2 
-13-3 
+10.4 

-2.8 


Shanghai. . . . 


1874-81 
1882-88 
1889-93 


91 

7-5 
7.0 


5.8^ 
5-8 


-1-4 
+1.3 
-0.9 



Here we find our theory confirmed in three out of 

four cases for India, two out of three for bank rates in 

Japan, and two out of three for market rates, one out of 

two for bank rates in China, while the one case for 

market rates is neutral. 

'This table is constructed from the data given in the Appendix. 
The entry marked (i) is for 1885-88, not 1882-88. 



66 American Economic Association. [408 

Summarizing the cases for the seven countries exam- 
ined, we find 57 favorable, and 16 unfavorable, to our 
theory, distributed as follows : 





Eng- 
land. 


Ger- 
many. 


France. 


United 
.States. 


India. 


Japan. 


China. 


Total 


Favorable . . 


21 


12 


8 


8 


3 


4 


I 


57 


Unfavorable . 


5 


3 


2 


2 


I 


2 


I 


16 



We therefore conclude with great confidence that, 
" other things being equal," the rate of interest is high 
when prices are rising and low when prices are falling. 



We turn next to the question hozv far the rate of in- 
terest has been adjusted to price movements. The for- 
mula (1 + /)=(! + 2 )(i +'^) or its more convenient 
form for present purposes, / ^ / + « + ia., enables us to 
calculate the rate of interest in the commodity standard 
which was equivalent to the money interest paid in each 
period. Thus in London for 1826-29 the rate of inter- 
est ( z ) in money was 3.5 %, but money was appreciating 
relatively to commodities 4.2 ^ ( « ), so that the interest 
actually paid in terms of commodities (z. ^., the forty 
commodities averaged by Jevons) was / = .035 + .042 
+ .035 X .042 = 7.8^. It will be seen from the table 
in § 3 that the virtual rate of interest paid in commod- 
ities usually varies inversely with the rate paid in money. 
For 1853-57, money interest was 5.3% and for 1891-95, 
1.6^ but commodity interest for 1853-57 was 2.8^ and 
for 1891-95, 5.5^. Moreover commodity interest fluc- 
tuated much more than money interest, the mean varia- 
tion from the average being for money interest .7 ^, and 
for commodity interest, 2.6^. All these facts suggest, 
— indeed practically demonstrate — that money interest 
was not adequately adjusted. It is of course not to be 



409] Appreciation arid Interest. 67 

assumed that commodity interest ought to be invariable, 
but we can be practically certain that its variations ought 
not to be three and a half times the variations in money 
interest. Such fluctuations must mean that the price 
movements were inadequately predicted. If any doubts 
were possible on this point they must disappear when 
we find that for 1871-73 commodity interest was minus 
2.7^. Money lenders would have been better off had 
they simply bought commodities in 1871 and held them 
till 1873. Such losses are especially apt to appear in 
short periods. Thus if we take the period 1824-25, we 
find that the market rate was Z-l%i ^^^ '^^te of appreci- 
ation was minus 14.5% and the virtual rate of interest 
in commodities minus 11. 2,%. 

The same observations apply to the rates at Berlin, 
Paris, New York, Calcutta, Tokyo and Shanghai. In 
New York during the inflation period 1861-65, com- 
modity interest sank to the fabulously low figure of -14.8 
fo , though the rate of interest in the labor standard was 
only -3. 1 fo . This shows in a striking way how thor- 
oughly the greenback inflation upset all business cal- 
culations. This fact has generally been recognized, 
though probably underestimated. It is amply confirmed 
by examining the predictions as to the termination of 
the war and the reduction of the gold premium which 
were recorded from month to month in the " Notes on 
the Money Market " in the ( New York ) Banker's Maga- 
zine. In all probability this is always true of pe- 
riods of paper money inflation. Our tables show it for 
the Japanese inflation of 1878-81. 

§7 

We can now understand why a high rate of interest 
need not retard trade nor a low rate stimulate it. These 



68 American Economic Association. [410 

facts have puzzled many writers. For instance,' " Public 
inquiry has been of late strongly directed to the reasons 
for the very low rate of interest upon loanable capital 
in the year 1875, the more especially as ten years ago 
the very high rates then prevailing created equal sur- 
prise. " Again,^ " The effect of such and many more 
changes effected during the last twenty years or so, is 
seen in a general increase in wealth and of mercantile 
industry and profits. Thus only can be explained the 
extraordinary high rate at which the interest of money 
has in the last ten years often stood. During 1854-57 
the rate of interest was only for a few months below 
5 fc , but for many months above it. For more than half 
a year it stood at 6 and 7^, and in the end of 1857 it 
remained for nearly two months at \o%. Again, in 
1861, interest rose to 6 and 8^, and all this, to the S2ir- 
prise of the elder generation.^ without the general stop- 
page of trade., the breach of credit., and the flood of 
bankruptcy., which has hitherto attended such rates of in- 
terest. It is certainly not to increasing scarcity of cap- 
ital we should attribute such rates, but rather to a greatly 
extended field for its profitable employment. " ^ But 
were these rates high ? If we turn to our table for Lon- 
don rates we find that the average market rate for 
1853-57 ^o^s appear to be the highest in the table but, 
unmasking it of the money element, we find it is 
equivalent to a commodity interest of 2.8^. This is 
i.o^ lower than the average for the whole period, 1826 
-95. Should we be surprised that industry did not lan- 
guish ? 

'Robert Baxter, Journal of the Royal Statistical Society, June, 1S76. 

'^Jevons, " Investigations, " p. 95. The italics are the present 
writer's. 

^This view had also been expressed by TookeandNewmarch, " His- 
tory of Prices ", Vol. V, p. 345. 



41 1] Appreciation and Inte^'est. 69 

Professor Bonamy Price^ writing at a time of very low 
interest rates says : " Everyone remembers the agitations 
associated with 7^, the trepidation of merchants, the 
apprehension of losses in business. ... If only a 
moderate rate could be reckoned on as steady, how happy 
would everyone have been ! . . . Yet what are the facts 
and feelings today? Is every merchant, every manu- 
facturer rejoicing in the pleasant terms on which he ob- 
tains the accommodation so necessary for his business ? 
. . . Alas ! no such sounds meet our ears. . . . Com- 
mercial depression is the universal cry, depression prob- 
ably unprecedented in duration in the annals of trade, 
except under the disturbing action of a prolonged war. 
In the export figures, the writer still fails to see 
any signs of the long-looked-for revival of trade. Both 
quantities and values continue to shrink in all save a few 
cases. . . . What then is the cause ? The explajta- 
ation will certainly not be found in gold nor in any form 
of currency whatever. . . . nor has anyoize said 
anything so ridiculous. . . . That cause is one and 
one only : over spending. " 

If we turn back to our London table we find, however, 
that for 1874-79 the commodity rate of interest was 
7. 1 % ! It would be astonishing if trade did not shrink 
under such a burden. 

All these writers mistook high or low nominal inter- 
est for high or low real interest. Tooke apparently did 
the same. In his " History of Prices ", vol. ii, p. 349, 
he names as the last of six reasons for the fall of prices 
for 1814-37, "a reduction in the general rate of inter- 
est. " This is probabl}^ not only an inversion of cause 
and effect, but also, when the veil of money is thrown 

1" One per cent ", Contemporary Review, April, 1877. The italics 
are the present -writer's. 



70 



American Economic Association. 



[412 



off, a mis-statement of fact. The commodity interest for 
1826-29 was 7.8%. It Avould seem that Tooke, Price, 
and Jevons all overlooked the fact that interest, unlike 
prices, is not an instantaneous but essentially a time phe- 
nomenon. 

§8. 

In order to make our results as certain as possible, the 
following table is formed in which the longer price 
movements are selected. It consists of three periods, of 
ten, twelve, and twenty-one years respectively. 

LONDOISr MARKET RATES OF INTEREST IN REI^ATION TO RISING 
ANT) FALLING PRICES, WAGES, AND INCOMES.i 





Market 

interest. 

i 


Apprecia- 
tion of 
Money in 
Commod- 
ities. 
a 


Virtual 
interest 

in 
commod- 
ities. 
/ 


Apprecia- 
tion of 

Money in 
Labor. 

a 


Apprecia- 
tion of 
Money in 
Income. 

a 


Virtual 
interest 

in 
Labor. 

y 


Virtual 
interest 

in 
Income. 

J 


1826-35 
1853-64 
1874-95 


3-4 
4.6 
2.4 


+ 1.2 
-0.9 

-1-2.4 


4.6 
3-7 
4-9 










1860-74 

1874-91 


4.0 
2.7 






— 2.1 
0.0 


-2.5 
—0.2 


1.8 
2.7 


1.4 
2.5 



In averages covering so many years, we may be sure 
that accidental causes are almost wholly eliminated. 
We find that during the period of rising prices, 1853-64, 
the average rate of interest was 2.2^ above the average 
for the subsequent period of falling prices, 1874-95, and 
1.2^ higher than in the former period of falling prices, 
1826-35. The rates in the commodity standard how- 
ever vary in the inverse order, the highest interest being 
for 1874-95 and the lowest for 1853-64. It is a note- 
worthy fact, in strong contrast with what we have found 

' The rates of appreciations in labor and income are based on 
" Changes in average wages in the United Kingdom between i860 
and 1 89 1," by A. L,. Bowley, in the Journal of the Royal Statistical 
Society, June, 1895. 



413] Appreciatio7i and Interest. 71 

true of sliort periods, that the commodity interest in this 
table of long periods is less variable^ than the money 
interest. Thus the adjustment of (money) interest to 
long price movements is more perfect than to short. 

§9. 

The foregoing table shows exactly how the English 
borrower has fared so far as commodities and labor are con- 
cerned. During 1853-64 he paid 2^-1% in commodities 
but during 1874-95 he had to pay 4.9%, an increase of 
1.2%. In the labor standard, during 1860-74, he paid 
1.8%, and during 1874-91, 2.7%, showing an increase of 
.9%, while in the income standard the rates were 1.4%, 
and 2.5% respectively, showing an increase of 1.1%. 
Now it is quite conceivable that commodity interest 
should normally be high during the latter period, if this 
period can be shown to be one of unusually rapid 
economic progress.^ That this was in fact the case has 

^ The mean variation for the three money rates is easily seen to be 
.8% and for the commodity rates only .5%. The two "labor" and 
" income" rates differ by .9 and 1.1% while the money rates differ 
by 1.3/3- In the New York table which follows, the money rates 
differ by 3.0% and the commodity rates by 3.2%, but the labor rates 
by only 2.2%. 

'-^ For when the future seems a time of relative plenty, future goods 
may be discounted at a high rate and profits measured in commodi- 
ties may be large. Contrariwise during a period of progressive 
scarcity commodity interest may be normally low. These theories 
may seem to conflict with current opinion ; but only when the funda- 
mental distinction is overlooked between a period of plenty and a 
period of progressive plenty, and between a period of scarcity and a 
period of progressive scarcity. During stationary scarcity and 
stationary plenty, normal commodity interest may be high and low 
respectively. But during the transition from scarcity to plenty in- 
stead of running through the intermediate rates, commodity interest 
may be normally higher than in either of the extreme states. This 
is a case in which " dynamic" economics differ strikingly from 
"static" economics. 



72 American Economic Association. [414 

been pretty thoroughly established by the admirable 
researches of David A. Wells ^ and others, and by the 
statistics of wages compiled by Falkner ^ and Bowley." 
But these considerations can scarcely apply to " labor 
interest" or " income interest." A man who borrowed 
the equivalent of a hundred days' income during 1860-74 
could pay it back in a year with the equivalent of 101.4 
days' income, while during 1874-91, for a similar loan 
he must return 102.5 days' income. This is the opposite 
of what we should expect as the influence of prog- 
ress. It therefore seems safe to ascribe at least 1.1% 
as the borrower's loss since 1874, compm^ed with his 
gain or loss before 1874. It may well be that part 
of this comparative loss for 1874-91 represents a gain 
for 1860-74. If we ascribe half to this gain, there 
remains the other half, .5% or .6%, as loss during 
1874-91. Although this division is quite arbitrary 
the conclusion that the borrower's loss was at least 
Yz'^/o seems reasonable when we consider that the 
total comparative loss, 1.1%, was itself a minimum. 
But even if we suppose the debtor's gain during the 
former pferiod twice his loss during the latter, (a supposi- 
tion which, in view of all the facts, must be within the 
claims of all reasonable monometallists) we still have a 
minimum (English) debtor's loss since 1874 of ^%. 

Combining the results just given with those of Chap- 
ter IX we see that the average loss to English borrowers 
during the fall of prices since 1874-75 probably lies be- 

' " Recent Economic Changes," (New York, 1890). 

^ Lac. cit. These statistics, taken in connection with price statistics, 
show that commodity wages, i. e., money wages divided by the index 
number of prices (z£/Ao/(?5a/^ unfortunately), rose in England during 
1860-74 at the rate of 1.8% per annum and during 1874-91 at the rate 
of 2.2%, while in America for 1849-57 they fell 2.7% per annum and 
for 1875-91, rose 2.4% per annum. 



415] Appreciation and Interest. 73 



tween yi'^/o and ^% and almost certainly between ]A,^o 
and 1%. The former result may be stated thus, 
y^± yi% and the latter, ^ d= >^%. We may therefore 
say with considerable confidence that the average debt- 
or's loss in England for contracts made since 1874-75, 
has been two-thirds of one per cent, per annum with a 
possible error of one-third of one per cent. In other 
words, the average debtor's loss could have been cor- 
rected by a reduction in the rate of interest of from 
one-third of one per cent, to one per cent. 

§ 10. 

For contracts made before 1874, but continued to the 
present, the loss, since 1874, must have been greater. 
We may therefore accept the former estimate of ^ % as a 
lower limit or, to be safe, 5^ %. To find an upper limit, 
we recur to the fact that India gold bonds purchased 
prior to 1875 yielded very nearly ^ % more interest than 
the average subsequent to that date. Since we have 
estimated that the average from 1875 was at most i % 
too high, the average for periods beginning before but 
ending after 1875, must have been at most i ^ % too high, 
for it can scarcely be claimed that the rate of interest for 
the part of the term of the bonds previous to 1875 ought 
to have been lower than that for the part subsequent to 
that date. We therefore conclude that, for English con- 
tracts made before 1874-75, the debtor's loss since 1874- 
75 has been between ^% and i>^%, i- <?., i d= ^%. 

It follows that for contracts which were made prior to 
1874-75 but subsequently converted or continued at a 
lower rate of interest, the loss since 1874-75 was 
I d= >^% per annum to the date of conversion and 
^ d= >^ % since that date. 



74 



American Economic Association. 



[416 



It should be observed that the foregoing calculations 
are based on public prices of bonds and rates on money. 
Interest on private loans and farm mortgages, although 
influenced ^ by the same causes which affect the money 
market, is less flexible and the debtor's losses or gains 
in these cases are doubtless somewhat greater. 



§11. 



The following table gives the long time averages for 
New York. The war period is omitted and a nine years' 
period of rising prices is compared with a seventeen 
years' period of falling prices. 

NEW YORK RATES OF INTEREST IN REI.ATION TO RISING AND 
FALLING PRICES AND WAGES. 



Interest Appreciation 

Prime of money 

Two name | in 

60 days. jcommodities. 

i a\ 



Appreciation 
of money 



labor. 



Virtual 
Interest 
in com- 
modities. 

j\ 



Virtual 
Interest 



labor. 
h 



1849 - 57 • 
1875-91 . 



8.2^ 
5-2 



-3-8 
+2.0 



-I.I 
-0.4 



4.1 
7-3 



7.0 
4.8 



We find for 1849-57 and 1875-91 that the money rates 
were 8.2 and 5.2%, the commodity rates 4.1 and '].'^%^ 
but the labor rates 7.0 and 4.8%. We see therefore, 
that in terms of labor, loans in America have actually 
been easier during 1875-91 than during 1849-57. This 
fact suggests the conclusion that the debtor's loss in 
America has not been as great as in England. This, if 

^ See Appendix, \ 2, 4th title. 

'^The average of Elliott's figures (which are not for "prime" paper) 
is 9.2, but i.o has been deducted from this average in order that it 
may be properly compared with the average of Robbins' figures for 
1S75-91. The correction is based on the fact that i.o was the average 
excess of Elliott's figures over Robbins' during the fifteen years, 
1860-74. See Appendix. 



417] Appreciation and Interest. 75 

true, may be due to a more rapid rate of progress in the 
United States/ 

§ 12. 

Four general facts have now been established : 
(i) High and low prices are directly correlated with 
high and low rates of interest ; (2) Rising and falling 
prices and wages are directly correlated with high and 
low rates of interest ; (3) The adjustment of interest to 
price (or wage) movements is inadequate ; (4) This ad- 
justment is more nearly adequate for long than for short 
periods. 

These facts are capable of a common explanation ex- 
pressing the manner in which the adjustment referred to 
takes place. Suppose an upward movement of prices 
begins. Business profits (measured in money) will rise, 
for profits are the difference between gross income and 
expense, and if both these rise, their difference will also 
rise. Borrowers can now afford to pay higher " money 
interest." If, however, only a few persons see this, the 
interest will not be fully adjusted ^ and borrowers will 
realize an extra margin of profit after deducting interest 
charges. This raises an expectation of a similar profit in 
the future and this expectation, acting on the demand for 
loans, will raise the rate of interest. If the rise is still 

^ See page 72, note 2. 

^ It seems scarcely necessary to add as an independent cause of mal- 
adjustment the accumulation (or in the opposite case, depletion) of 
bank reserves, for this is but another symptom of mal-adjustment due 
to imperfect foresight. An increase of gold supply, as in 1852-53 
(see Tooke and Newmarch, "History of Prices," vol. V, p. 345) 
may first find its way into the loan market instead of into circulation. 
But if foresight were perfect, this would not happen, or if it did hap- 
pen, borrowers would immediately take it out (or increase the liabil- 
ities against it) to avail themselves of the double advantage of low 
interest and high prospective profits from the rise of prices about to 
follow. 



76 American Economic Association. [418 

inadequate the process is repeated and thus by continual 
trial and error the rate approaches the true adjustment 

When a fall of prices begins, the reverse effects ap- 
pear. Money profits fall. Borrowers cannot afford to 
pay the old rates of interest. If, through miscalculation 
they still attempt to do this, it will cut into their real 
profits. Discouraged thus for the future, they will then 
bid lower rates. 

Since at the beginning of an upward price movement, 
the rate of interest is too low, and at the beginning of a 
downward movement it is too high,^ we can understand 
not only that the averages for the whole periods are im- 
perfectly adjusted but that the delay in the adjustment 
leaves a relatively low interest at the beginning of an 
ascent of prices and a relatively high interest at the be- 
ginning of a descent. This would explain, in part at 
least, the association of high and low prices with high 
and low interest.^ The fact that the adjustment is more 
perfect for long periods than for short, seems to be be- 
cause in short periods, the years of non-adjustment at 
the beginning occupy a larger relative part of the whole 
period. 

§ 13- 

What has been said bears directly on the theory of 
"credit cycles." In the view here presented periods of 
speculation and depression are the result of ifiequality 
of foresight. If all persons underestimated a rise of 
price in the same degree, the non-adjustment of interest 
would merely produce a transfer of wealth from lender 
to borrower. It would not influence the volume of 
loans (except so far as the diversion of income from one 
person to another would itself have indirect effects, such 

' These facts may be verified from the tables in the Appendix. 
-" Cf. I 2. 



419] Appreciatio7i and Interest. 77 

as bankruptcy). Under such circumstances the rate of 
interest would be below the normal, but as no one knows 
it, no borrower borrows more and no lender lends less 
because of it. In the actual world, however, foresight 
is very unequally distributed. Only a few persons have 
the faculty of always " coming out where they look." 
Now it is precisely these persons who make up the bor- 
rowing class. Just because of their superior foresight 
society delegates to them the management of capital. 
It is they who become "captains of industry." Their 
share consists of profits (or losses) while others lend 
them capital and receive interest or commuted profits/ 
It therefore happens that when prices are rising, bor- 
rowers are more apt to see it than lenders. Hence, 
while the borrower is willing to pay a higher interest 
than before for the same loan, lenders are willing to loan 
the same amount for the same interest. That is, the 
" demand schedule " ^ will rise while the " supply 
schedule " remains comparatively unchanged. This 
will of course raise the rate of interest. But it will also 
cause an increase of loans and investments.^ This con- 
stitutes part of the stimulation to business which bi- 
metallists so much admire. 

When prices fall, borrowers see that they cannot em- 
ploy " money" productively except on easier terms, but 
lenders do not see why the terms should be made easier. 
In consequence " entrepreneurs" borrow less, enterprise 

^ Hadley, " Interest and Profits," Annals of the American Acade- 
my of Political and Social Science , November, 1893; also "Econom- 
ics," (New York, 1896), pp. 116, 269. 

^Marshall, "Principles," Vol. i, (3rded.) p. 171. 

^ That this and the corresponding statement in the next paragraph 
are borne out by facts appears to be confirmed, so far as bank loans 
and discounts are concerned, by Sumner, "History of Banking in 
the United States," (New York, 1896) and Juglar, " Crises commer- 
ciales," (Paris, 1889). 



78 American Economic Association. [420 

languishes and, though interest falls in consequence of 
decrease in demand, it does not fall enough to keep the 
demand from decreasing/ 

If lenders, as a class, were possessed of greater fore- 
sight than borrowers, we should find trade languishing 
during rising prices and stimulated during falling prices. 
In the former case lenders would require high interest 
for fear, as in 1871-73, they were lending at a loss of 
real wealth, while borrowers would be afraid of the ap- 
parently high rates charged ; and in the reverse case 
lenders would be eager to reap the benefits of an appre- 
ciating standard while borrowers, deceived by the appar- 
ently low rates, would rush in to profit by them. 

We see therefore, that while imperfection of foresight 
transfers wealth from creditor to debtor or the reverse, 
inequality of foresight produces over-investment during 
rising prices and relative stagnation during falling prices. 
In the former case society is trapped into devoting too 
much wealth to productive uses and in " long production 
processes " ^ while in the contrary case under-in vestment 
is the rule. It does not seem possible to decide the ques- 
tion which of the two evils is the greater. ^ 

^ President Andrews in "An Honest Dollar," p. 3, writes : "Interest 
is low . . not because money is abundant as before, but because it is 
not, its scarcity having induced fall of prices and so paralysis in in- 
dustry." But it should be added, the cause of the fall of interest is 
primarily the expectatio7i of small profits. Cf. infra. 

- Professor Bohm-Bawerk, (" Positive Theory of Capital, " p. 335), 
writes : " Now the constant presence of the agio on present goods is 
like a self-acting drag on the tendency to extend the production pe- 
riod. Extensions which would be harmful as regards social provis- 
ion are thus made economically impossible. " During rising prices 
this drag presses too lightly and during falling prices too heavily. 

■^ Bimetallists usually claim that falling prices are the greater evil . 
For arguments on both sides see Professor Marshall's evidence, 
Report on Depression of Trade, (1886), p. 422. 



42 1] Appreciation and Interest. 



79 



It is believed that the foregoing theories correspond 
closely with observed facts as to business stimulation 
and depression, volume of loans, etc., but it is not pro- 
posed here to enter upon a special statement of them/ 

Nor is this the place to treat fully the reaction on prices 
themselves. But it can scarcely be doubted that the 
mal-adjustment of interest is a central feature in the 
whole movement. Professor Marshall, who recognizes 
fully the distinction between money and commodity in- 
terest, says : ^ " When we come to discuss the causes of 
alternating periods of inflation and depression of com- 
mercial activity, we shall find that they are intimately 
connected with those variations in the real rate of inter- 
est which are caused by changes in the purchasing 
power of money. For when prices are likely to rise, 
business is inflated, and is managed recklessly and waste- 
fully ; those working on borrowed capital pay back less 
real value than they borrowed, and enrich themselves at 
the expense of the community. When afterwards credit 
is shaken and prices begin to fall, everyone wants to get 
rid of commodities and get hold of money which is rap- 
idly rising in value ; this makes prices fall all the faster, 
and the further fall makes credit shrink even more, and 
thus for a long time prices fall because prices have 
fallen." 

We would add that these effects of credit could not 
follow if the interest rate were perfectly adjusted. In- 
terest, rather than credit, appears as the chief independ- 
ent variable, objectively speaking, though behind it all 
is imperfection of foresight. 

^See Report on Depression of Trade, 1886; and Report of the 
Gold and Silver Commission, 1888. 

2 " Principles of Economics ", Vol. I, (3rd ed., 1S95), p. 674. 



PART III. APPLICATIONS. 
CHAPTER XL 

THE BIMETALLIC CONTROVERSY. 
§1. 

It is not the purpose here to follow all the arguments 
for and against bimetallism, but merely to outline the 
bearing of the foregoing theories and facts upon some of 
those arguments. 

We have seen in theory and in practice that the rate 
of interest has tended to accommodate itself to the 
changing value of money. It follows that it is quite er- 
roneous to obtain the amount of the debtor's or creditor's 
loss by merely reckoning the effect of appreciation or 
depreciation on \}i\^ principal of the debt. 

And yet, after all allowances are made, it is true that 
there remains a net loss alternating between debtors and 
creditors according to the varying tides of credit and 
prices. During the last twenty years it has happened 
that the debtor was on the losing side. We have estimated 
his average loss at ^ + ^ % per annum in England and 
probably less in this country. This loss is not inconsid- 
erable. When looked at in the aggregate it appears 
very large indeed. The minimum net indebtedness 
public and private in the United States is given at 20 
billions,^ on which ^% would amount to 130 millions 
per annum. But when we compare this with the aggre- 

' G. K. Holmes, Bulletin of the Department of Labor, November, 
1895, p. 48. 



423] Appreciation and Interest. 81 

gate principal involved or with the 14 odd billions ^ of an- 
nual product, it does not seem capable of the deep social 
harm attributed to it. In fact it is always misleading to 
consider aggregates except in comparison with each 
other. Applied to an ordinary two months' loan of 
$1,000, % % amounts to one dollar. In New York city 
the up-town banks often charge a rate more than ^ ^ 
higher than that of the down-town banks without driving 
away customers. 

§ 2. 

The ordinary estimates of the debtor's loss are based on 
index numbers. From Sauerbeck's tables it appears that 
between 1873 ^^^ ^895 money appreciated in terms of the 
commodities selected, 79.0%, which is at therateof 2.7% 
per annum. This is from three to eight times as much as 
the estimate we have made. The error of the ordinary 
calculation does not consist simply in neglecting the 
matter of interest. The use of index numbers is itself 
subject to fatal objection.^ When unchecked by other 
statistics they are very misleading. Not only do we 
reach different results according to the number of com- 
modities and the method of averaging,^ but the very best 
methods fail to give a trustworthy measure of ordinary 
domestic purchasing power, both because they are based 
on wholesale instead of retail prices and because they 
ignore expenditure for house rent and for labor and 
domestic service, which, in the family budgets of those 
who borrow and lend, must form a very large item. 

^ Edward Atkinson, Engineering Magazine, December, 1895. 

^ The reader is reminded that, though we have used index numbers 
to determine " commodity interest, "^we have not employed them to 
estimate the debtor's loss. 

^See articles by Edgeworth, Sauerbeck and Pierson in the ^co«o w«^ 
Journal, March, June, and September, 1895, and March, 1896. 



82 American Economic Association. [424 

Moreover to know the purchasing power of a dollar does 
not enable us to know the " subjective value" or mar- 
ginal utility of money. The number of dollars at com- 
mand ( /. ^., money incomes) must also be considered. 
And even were our knowledge complete as to the 
marginal utility of money as well as its purchasing 
power, we should be as far as ever from solving the 
problem of the debtor's loss. The question is not one 
of appreciation of gold relatively to commodities or to 
labor or any other standard. It is, as we have seen, 
exclusively a question of foresight and of the degree of 
adaptation of the rate of interest. 

§3- 

It scarcely needs to be pointed out that bimetallism 
can only affect unpaid debts. We should therefore 
clearly recognize the fact that the most of the loss which 
debtors have suffered since 1873 has already passed be- 
yond the reach of remedy. Of the residuum the losses 
vary with the duration of the debt. On debts three 
years old the loss in England is probably about two per 
cent., on those six years old about four per cent., and so on. 
Moreover, on debts contracted before the fall of prices 
began, the annual rate of loss was greater, being proba- 
bly, as we have seen, i ± /^%. Most such debts, how- 
ever, including even national debts, have received part 
of the benefit of low interest through extensive con- 
versions. 

Now bimetallism, if adopted, so far from rectifying 
gains and losses, would simply increase the inequalities. 
If it resulted in debasing the standard ten per cent, it 
might exactly remedy debts fifteen years old, but the 
correction would be too small for those older and too 



425] Appreciation and Interest. 83 

large for those younger than fifteen years. The latter 
form the great bulk of existing indebtedness. The 
average life of a farm mortgage is 4^ years ^ so that 
the average age of mortgages now in force would be 
about ^Yi years. Bank loans run only a few days or 
months. These and other short time loans make up 
some sixty per cent, of existing indebtedness.^ The re- 
mainder consists of railway and government loans and 
few of them extend back to 1873.^ '^\i^ chief and 
dominant effect of debasement would therefore be to 
defraud the lender of today and yesterday.* The older 
debts, for which the remedy is designed, no longer exist. 

§4. 

But even if bimetallism or any other financial scheme 
could so scale debts as exactly to counteract the losses 
connected with the fall of prices, the ethics of such an 
arrangement ought not to go unmentioned. The fact 
that debtors have lost does not imply that they have suf- 
fered an injustice. If a man insures his house and it 
burns the next day the insurance company suffers a loss 
but not an injustice. If the company should ask for leg- 
islative relief on the ground that it had not expected so 
sudden a termination of its policy, that the fire was 
brought about by causes which it could not possibly 
foresee or provide against, it would be laughed to scorn. 
" Keep your contract " would be the reply. It would 
^ 'Eleventh Census, Bulletin 71. 
'^Holmes, loc. cit. 

^ Probably mucb less than one- fourth for American railways. This 
estimate is made by looking over all the funded indebtedness whose 
dates of issue are given in the " Ofl&cial Intelligencer" for 1894. 

* For effects on "Social Classes," see article by Professor H. W. 
Farnani, Yale Review^ August, 1895, p. 183. 



84 American Economic Association. [426 

make no difference if the fires were nniversal, and every 
insurance company lost. Those who assume the risks 
must take the consequences. A farmer mortgages his 
farm and agrees to pay $1,000 and 5% interest. By the 
terms of the agreement he takes all risks as to what the 
dollar will buy of wheat or anything else. He may lose 
and all farmers may lose and the causes may be in India 
or Australia or in the sun spots, but we can scarcely af- 
ford to surrender the ancient principle of the Inviolabil- 
ity of Contracts, through sympathy with the misfortunes 
of any individual man or group of men. That elements 
of risk exist in every contract and that this risk implies 
responsibility are too often ignored. President Andrews 
writes ^ : " Increase in the value of money robs debtors. 
It forces every one of them to pay more than he cove- 
nanted [!] — not more dollars but more value." But 
contracts which call for money do not call for " value " 
any more than contracts to deliver wheat call for money. 
If a man had agreed a year ago to deliver 10,000 bricks 
to a builder at a fixed price, he would not be justified in 
offering only 9,000 on the ground that the price had 
gone up. A contract to pay " value " would be a legal 
curiosity, and the court which should attempt to inter- 
pret it would hear an interesting assortment of defini- 
tions from our leading economists. 

Closely associated with the principle of the Inviolabil- 
ity of Contracts is the principle against retro-active 
laws, and in particular, against laws which alter existing 
contracts. The world has reached these principles 
through a long and weary struggle and much costly ex- 
perience with repudiation and the abuses of legal tender. 
The burden of proof rests on those who would revert 
^ " An Honest Dollar, "p. 2. 



427] Appreciation and Interest. 85 

to these experiments for the sake of any benefits from 
bimetallism. Surely the practical reasons against such 
a course are obvious enough. When once a government 
has undertaken to " correct " debtor's losses, it will not 
stop at one attempt. History teaches that a nation once 
embarked on such a policy never keeps its most solemn 
word as to where it shall leave off. ^ Creditors will fear 
to lend except at usurious rates and the debtor of the fu- 
ture will pay dearly for the emancipation of the debtor 
of the present.^ 

§5- 

To those who claim that the cause of the aggravation 
of debts was governmental action in the first instance 
and that therefore it is now a fit subject for governmental 
correction, the obvious answer is that this does not ap- 
ply to the great mass of existing contracts which have 
been formed since demonetization. 

Finally it may be objected that the gold standard as 
such is on the side of creditors as against debtors because 
it is an appreciating standard and according to our own 
statistics the debtor usually wins in rising and loses 
in falling prices. 

Such reasoning, however, is entirely fallacious. The 
fallacy is of the same kind as that contained in the fa- 
cetious advice to young speculators : " Buy when stocks 
are low and sell when they are high. " It is easy to 
prophesy after the event ; investors in India silver bonds 
have lost for twenty years but this does not prove that 
the present price of rupee paper is still too high. If it 
did, London brokers would be the first to know it and 

1 Shaw, " History of the Currency," (18951 ; also Sumner, " History 
of American Currency," p. 331. 

2 See the writer's "Would Bimetallism benefit the 'Debtor Class'?" 
The Bond Record, April, 1896. 



86 American Economic Association. [428 

correct it. We cannot therefore say the " present 
arrangement is all in favor of tlie creditor and against 
the debtor. " What bimetallist will risk his reputation 
in predicting the course of prices and interest in the 
next twenty years ? If prices rise, we may with great 
probability predict that the debtor will vrin. If they 
fall, he will lose. But who knows which is the true 

§6. 

Legislation to offset the effects of a fall of prices in 
the past is wrong, because retro-active. Legislation to 
offset the effects of a fall in the future is absurd, because 
we cannot know there will be a fall, and if we could, 
there would be no need of legislation. 

There remains to be considered legislation for the 
purpose of making the monetar}- unit less variable, that 
is, not to prevent something which we can foresee but 
to prevent something which we cannot foresee. Such 
a reason for monetan,- legislation must be recognized 
at once as thoroughly sound. But it applies equally 
well to " symmetallism" ^ and other plans - for monetary 
reform. 

That bimetallism ( as long as it lasted)^ would be 

' Edgewortli, " Thoughts on monetary reform", Economic loiirnal, 
September, 1S95. 

'E.g., the multiple standard propounded by Lowe, 1S22, and 
Scrope, 1833, and advocated by Jevor.s, "Money and the Mechanism 
of Exchange", p. 328, and "Investigations", p. 123, and by Marshall, 
Report of the Commission on Depression of Trade, p. 423 ; also 
the various forms of double standard suggested by Marshall, ibid., 
Edgeworth, ibid., Hertzka " Das iuternationale Wahrungsproblems," 
1892, and Stokes, "Joint Metallism," (1S95) ; also the various forms of 
elastic currenc}* suggested by Professor Walras, " Theorie de la 
Monnaie", (Lausanne, iSS5i, by Secretary Windom and others. 

'See the writer's " Mechanics of Bimetallism," Economic Journal, 
September, 1894. 



429] Appreciation and Interest. 87 

more dependable than monometallism is probable on 
a priori grounds, but the statistics which we have given 
seem to reveal as great uncertainty in price movements 
before 1873 ^^ since. It is indeed a large question 
how far au}^ sort of monetary' reform could remedy the 
matter ; for the expansion and contraction of credit 
might be almost as violent and mischievous as ever. It 
may be however, that " the evils . . are so great that it 
is worth while to do much in order to diminish them a 
little." ^ If a more stable and less expensive ^ monetary 
standard can be found, it will be an inestimable boon to 
the civilized world. As an improvement on the two 
single standards now existing, bimetallism, launched at 
the market ratio, ma}" be worth serious consideration. 
But the proposal now before the world is bimetallism at 
15/^ or 16 to I. Such bimetallism means debasement 
of the standard of any single country- which attempts it. 
If international, it means debasement in gold standard 
countries, and a violent contraction and appreciation in 
silver standard countries. In no other wa}- could the in- 
fluence of the legal ratio on the market ratio be felt. We 
should witness not only losses to creditors in the former 
countries but losses to debtors in the latter, and these 
losses would be far in excess of those which we have 
found to follow from the slow" and half foreseen appre- 
ciation of the last tv^'enty years. 

'Marshall, "Principles of Economics" Vol. I, 3rded., (1895), p. 674. 

*Jevons, "Investigations," p. 104; " . . the very scarcity of gold 
is its recommendation . . in itself gold digging has ever seemed 
to me almost a dead loss of labor as regards the -world in general." 
Also Lexis, Economic Journal, June, 1S95, p. 276. 



CHAPTER XII. 

THE THEORY OF INTEREST. 

§1. 

The relation existing between interest and appreciation 
implies that the rate of interest is relative to the standard 
in which it is expressed. Economists, from Hume and 
Adam Smith down, seem to have considered the money 
element entirely eliminated from the rate of interest by 
the simple fact that, in the last analysis, it is capital, 
not money, which is loaned and returned. But, as 
has been seen, we can identify the rate of interest in 
terms of capital with the rate of interest in terms of 
money only when the price ratio between money and 
capital remains constant. 

The first thought suggested by this fact is to dis- 
tinguish between " nominal" and " real" interest in the 
same way that we distinguish between " nominal" and 
" real" wages. This seems to be the thought of all the 
writers who have touched on the subject. Professor 
Marshall in fact uses the words " real" and " nominal."^ 
de Haas speaks of the effect of the appreciation or de- 
preciation of money as introducing a " third element"^ 
into the rate of interest. This " element" is to be added 
to or subtracted from the sum of the other two elements, 
which are a payment for capital (or the rate of interest 
proper) and a payment for insurance. John Stuart Mill 

' "Principles of Economics," Vol. I, 3rd ed. (1S95), P674. 

''■Journal of the Royal Statistical Society, March, 1S89. It will 
be seen from the formula i-l-7"=(i + (i + a) that the "third 
element" is not a mere additive term. 



43 1] Appreciation aiid hiterest. 89 

and the eighteentli century pamphleteer ^ were evidently 
thinking of a normal rate of in terest in coin to which 
a certain extra charge is to be added if paper depreciates 
in reference to coin. Finally the article of Professor 
John B. Clark ^ is devoted chiefly to a search for an ab- 
solute standard to which we may refer any monetary 
appreciation or depreciation and in which therefore 
" real" interest could be expressed. It is not denied 
that the words " real" and " nominal" are very conven- 
ient terms and for a rough and ready expression may 
serve a useful purpose. But the mere distinction be- 
tween "real" and "nominal" is quite inadequate for a 
true and accurate statement of the case.^ 

If we seek to eliminate the money element by ex- 
pressing the rate of interest in terms of real " capital," 
we are immediately confronted with the fact that no two 
forms of capital maintain or are expected to maintain a 
constant price ratio. There are therefore just as many 
rates of interest on capital as there are forms of capital 
diverging in value. Even if we could find an ideal in- 
dex number for capital in general or for commodities, 
there are other kinds of interest which might also claim 
the title of " real " ; we refer to " labor" and " income"* 
interest. It cannot even be claimed that relative 
changes in prices, wages and incomes are abnormal phe- 
nomena, or incident only to a dynamic society. Even 
in the most ideal stationary state, the mere changes in 
seasons would make interest between summer and winter 

' See Chapter I, § 2. 

"^ Political Science Quarterly, September, 1895. 

* Professor Edgeworth ( " Variations in Value of Monetary Stand- 
ards", Report of the British Association for the Advancement of 
Science, 1889, p. 163), exhibits seven kinds of standards for deferred 
payments. 

* See Chapter X, ?? 8, 9. 



90 Ama-ican Economic Association. [432 

low in terms of summer precincts sncli as frnit, and high 
in terms of winter products such as ice. The rate of 
interest is, as Professor Bohm-Bawerk shows, an agio on 
present goods exchanged for future goods of the same 
kind. It is a simple corollary of this theorem, though 
Professor Bohm-Bawerk does not express it, that this 
agio may be in theory and must be in practice a different 
agio for each separate kind of goods. 

§ 2. 

But, it may be urged, surely there is some invariable 
standard conceivable in theory if not determinable in 
practice, which may serve for a base line of apprecia- 
tion and depreciation for all goods and money, and in 
terms of which we may express a "real" rate of interest. 
This brings us to the question of an absolute standard 
of value. But here we encounter another difficulty. 
Such an absolute standard will differ with each indi- 
vidual.^ The fact that a dollar is a smaller unit to a 
millionaire than to a poor laborer, has as its consequence 
that as the millionaire grows poorer his dollar grows 
larger while as the laborer grows richer his dollar grows 
smaller. On account of such changes in personal for- 
tunes the dollar, however defined, will be constantly 
appreciating and depreciating in different degrees among 
different men and classes. In fact the phenomenon of 
borrowing and lending is to some extent itself a conse- 
quence of the different degrees in which money appre- 
ciates or depreciates to borrower and lender. 

1 Marshall, "Principles," Vol. I, (3rd ed.), p. 198, and Royal Com- 
mission on Depression of Trade, 1SS6, p. 423 ; also the writer's 
"Mathematical Investigations in the Theory of Value and Prices," 
Transactions of the Connectictd Academy, (New Haven, 1892). 



433] Appreciation and hiterest. 91 



In addition to the differences already mentioned, there 
is a different rate of interest for each period of time con- 
sidered. The rate in any given goods for a loan con- 
tracted to-day and payable one year hence is the agio of 
this year's over next year's goods ; the rate for a -loan to 
be contracted one year hence and payable two years 
hence is the agio ( reckoned to-day ) of next year's goods 
over the goods of the succeeding year and so on. The 
rate for a loan contracted to-day and payable two years 
hence is the " actuarial average " ^ of the two previous 
rates. There is no reason why these three rates and 
others constructed in the same manner should not be all 
different.^ 

§ 4- 

We thus reach a multiple theory of interest. Our 
results are, first, that different standards have in general 
different rates of interest ; secondly, that of the numer- 
ous standards thus possible a different one is " absolute " 
for each individual ; thirdly, that in each standard there 
will be a different rate for dijfferent periods of time.^ 

' See Chapter V, § 4. 

"^ Professsor Bohm-Bawerk ( "Positive Theory, " p. 280 ), in showing 
how "arbitrage transactions" tend to equalize rates, tacitly assumes 
that the iirst two rates above mentioned are equal and only proves 
that in that case the third will be equal to the first. 

^ Besides these three sorts of variations there are others due to un- 
certainties of various kinds. In the theory of Part I, we have only 
considered the case where the relative divergence of two standards is 
foreknown with certainty. To complete the picture it is necessary to 
introduce the theory of probabilities as applicable to economics. 
(See Marshall's "Principles", p. 198, note, and 211, note.) When this 
is done it will also explain the diiferent terms for call loans, 30 days, 60 
days loans, etc., as well as for different degrees of security. Although 
in the latter case we may distinguish pure interest as the rate for per- 
fect security, yet the surplus above this sum is not simple insurance- 
It is not a certain sum paid for a contingent loss but it is itself con- 



92 American Economic Association. [434 

In actual business experience none of these three sorts 
of differences attract attention. The third is usually 
very slight in amount. ^ The second is not reducible to 
statistical measurement ; while the first escapes notice 
because of the habit of reckoning- always in money. In 
a few cases, as for Indian and Chinese bonds, London 
brokers must have occasion to note the fact that 3% in 
silver is usually not equivalent to 3 ^ in gold, but even 
in such cases the gold rate is thought of as " the " rate. 
So also speculative contracts in wheat, land, etc., and 
ordinary loans, which are really advances of stock, ma- 
terials, and other forms of capital, are always translated 
into money and their essential nature as involving inde- 
pendent standards is concealed. But the economist, who 
so often finds it necessary to forsake the language of 
money and speak in terms of the things which money 
measures, must here also recognize the fact that the rate 
of interest in terms of money is simply a common repre- 
sentative of multiform rates in other standards. 

These rates are mutually connected and our task has 
been merely to state the law of that connection. We 
have not attempted the bolder task of explaining the 
rates themselves. Such an explanation constitutes the 
" theory of interest " in the more usual sense and forms 
the subject of Professor Bohm-Bawerk's masterly trea- 
tise. The relation between the two branches of the sub- 
ject may be pictured as somewhat analogous to that be- 
tween the theory of relative prices and the theory of 
price levels. 

tingeut ; and, what is more important here, it is not a present sum but 
a series of deferred sums and as such is itself subject to the principles 
of pure interest. It follows that we cannot strike out the " insurance 
element " as a mere additive term with which the theory of interest 
proper has no concern. A complete theory has yet to be written. 

' For a supposable case of great variation, see Chapter V, ^ ? i, 2. 



APPENDIX. 

STATISTICAL DATA. 
§ I. 

The writer has found so much difficulty in securing 
a long series of yearly averages for rates on " money ", 
that the results are here presented in the hope that they 
may be of use to others. 



YEARLY AVERAGE RATES OF INTEREST ON " MONEY." i 



London 



Berlin. 



New York. 



Calcutta 



' (LI C rt I 



Tokyo. 



Shanghai. 



1824 
1825 
1826 
1S27 
1828 
1829 
1830 
1831 
1832 
1833 
1834 
1835 
1836 
1837 
1838 

1839 
1840 
1841 
1842 
1843 
1844 
1845 
1846 
1847 
1848 
1849 
1850 
1851 
1852 
1853 
1854 
1855 
1856 
1857 
1858 
1859 
i860 
1861 
1862 
1863 
1864 
1865 
1866 
1867 
1868 
1869 
1870 
1871 
1872 
1873 
1874 
1875 
1876 
1877 
1878 
1879 
1880 
188 1 
1882 
1883 
1884 
1S85 
1886 
1887 
ib88 
1889 
1890 
1891 
1892 

1893 
1894 
1895 



I 3-5 

3-9 

4-5 

3-3 

30 

3-4 

, 2.8 

! 3-7 

I 3-1 

! 2.7 

3-4 
3-7 
4.2 

4-5 
3-0 
5-1 
50 
4-9 
3-3 
2.2 
2.1 
3-0 
3-8 
5-9 
3-2 
2.3 
2.2 

3-1 
1-9 

3.7 
4-9 
4-7 
5-9 
7-1 
3.1 
25 
4.1 
5-5 
2.4 
4-3 
7-4 
4.6 
6.7 
2.3 
1.8 

3-0 
3-1 
2.7 
3-8 
4-5 
3-5 
3-0 
2.2 

2.3 
3-5 
1.8 
2.2 
2.9 
3-4 
3-0 
2.6 
2.0 

2-1 
2.4 
2.4 
2.7 

3-7 
2.5 
1-5 



3-9 
9-7 
6.5 
7.0 
6.1 

4-9 
4.2 
4.2 
5-1 
5-5 
8.7 
6.9 

9-1 
5-1 
5.8 
6.0 
5-7 
4-7 
50 
3-9 
6.2 

5-7 
6.8 
8.4 
5-3 
6.3 
4.6 
5-3 
6.6 
6.8 
6.4 
5-4 
6.0 
5-6 
5-5 
7.0 
5-8 
3-1 
3-5 
4-9 
5-4 
4-3 



iS. 


!i8 


14- 


18 


14- 


18 


14. 


14 


12. 


ii4 


12. 


'14 


12. 


i,S 


10. 


^3 


II. 


15 



11. |i6 

13- '17 

14- ;i7 
10. 17 

7.9 II 

12. 16 

13. II 
8.8 9 
9.0 8 

10. I 9 

TO. 10 

11. II 

9-4 9 

8.3! 8 
7.8i 7 

9-3; • 

9.6 . 



I The London, Berlin and Paris market rates are on first class merchants' 



437] Appreciation arid Interest. 95 

All the rates are entered in the foregoing table as 
rates of "interest," though the rates for the Banks of 
England, Germany and France are rates of discount. 
The two are not quite equivalent but, for the purposes 
of the foregoing work, the distinction between them is 
unnecessary because, in a continuous series, the error, if 
any, affects all items nearly alike and thus cancels itself 
out in the comparisons. 

Had it been necessary, some of the tables could have 
been extended back. Thus the Bank of England rate 
could be given to 1696 but it was too inflexible to be of 
use. The Berlin and Paris bank rates could also be ex- 
tended and the Paris market rate could be given from 
1861 (except for 1870 and 1871) from data in Wi^ Econo- 
mist. 

bills. The figures for 1824-58 are from the evidence of D. B. Chapman before the 
Committee on the Bank Act, 1857, Sess. 2, X, pt. I, p. 463, (also reprinted in 
Hunt's Merchants' Magazine. Vol. 41, (1859) P- 95)- Th"; remaining figures are 
compiled from the Economist. For those for 18S4-94, the writer is indebted to 
Professor F. M. Taylor of Michigan University, who had collected them, from the 
Economist for a different purpose. The Bank of England rates for 1824-43 are re- 
duced from Burdett's " Ofiicial Intelligencer," (1894), p. 1,771. The remaining ones 
for England, Germany and France are reduced from those given in the Report 
of the Royal Commission on Depression of Trade, 1886, p. 373, and the Economist. 
They represent the bank "minimum." The New York rates are taken, the first 
two columns, from a table by E. B. Elliott (afterward government actuary) in 
the (New York) Banker's Magazine, 1S74. The quotations given as "60 days" 
apparently included single name paper. The third column to 1890 is compiled 
from a diagram of highest and lowest monthly rates prepared at Yale college by 
Mr. G. P. Robbins of the class of 1891, and has been completed from the Financial 
Review, by averaging the highest and lowest weekly rates. It has been 
found impossible to extend the table back beyond 1849, as the rates are not 
systematically reported. The Calcutta rates are the minimum of the Bank of 
Bengal and have been kindly furnished by Messrs. Place, Siddons and Gough, 
brokers, of Calcutta. The market rates of Tokyo are averages of the highest and 
lowest rates of each year, furnished by Mr. Ichi Hara of the Bank of Japan, 
Tokyo. The bank rates are for the Tokyo and Yokohama Co-operative Bank and 
were translated by Mr. Sakata, student at Yale, from a history of Japan by 
Zenshiro Tsuboya. The tables for Shanghai have been procured through the 
kindness of Mr. F. W. "Williams of the department of Oriental History of Yale 
University, who obtained them from Mr. J. F. Seaman of Shanghai. The first 
column contains the rates ruling in the native market, and the second, those of 
the Hong Kong and Shanghai bank (under English control) on overdrawn cur- 
rent accounts, a species of demand loans and the ordinary form of lending in 
Shanghai. Mr. Seaman was told that the market rates cannot be extended back 
beyond 1S85, as the books of the Chinese banks for previous years are burnt. 

2 This rate is only from September when the operation of the Bank Act began, 
previous to this the custom of the bank was to have a uniform rate for all loans. 



gS American Economic Association. [438 

Many of the sources from which the table has been 
drawn also contain other information such as the rates 
for Vienna, Amsterdam and other money centres, the 
weekly or monthly rates, the variation with the seasons, 
the number of changes of the Bank Minimum, etc. 

§2. 

Of sources not mentioned in the above note, the chief 
which the writer has encountered are : 

Adolf Soetbeer, " Materiallen zur Wabrungsfrage," (Berlin, 1S86), 
p. 78. 

Covers 1851-S5 for Banks of England, France and Germany, and mar- 
ket rates of Hamburg and Vienna. 
Austrian Government, " Tabellen zur Wabrungsfrage," (Vienna, 
1S92), pp. 204-6. (A second edition bas just appeared, 1896). 
Covers 1S61-91 for banks of Italy, England, France, Germany, Austria, 
Belgium and Holland, and market rates in Vienna, iS6q-gi. 

W. Stanley Jevons, " Investigations in Currency and Finance," (Lon- 
don, 1884). 

Contains diagram for prices of consols and 3 per cent, stock from 1731, 
and minimum rate of interest in London from 1824 ; also monthly vari- 
ation in rate of interest, p. 10. The diagram for the price of consols 
shows that during the middle and first half of the eighteenth century 
the interest realized was almost as low as in the present generation. 
This was a period of falling prices. 
Eleventb Census of the United Slates, Bulletin 71 (on real estate 
mortgages, 1880-89). 

This is probably the most elaborate series of interest averages ever 
constructed. If these averages be compared with the course of prices 
during the average term of the contracts (five years), it will be found 
in nearly every case that interest is high or low according to the degree 
of the rise or fall in prices. 
"Viscomte G. D'Avenel, " Histoire economique de la propriety, des 
Salaires, des Denr^es et de tous les Prix en gdn^ral depuis I'an 1200 
jusqu'en I'an 1800," (Paris, 1894), vol. II, p. 882. 

This work contains also tables of the purchasing power of money, but 
neither the interest nor price statistics are sufficiently exact or detailed 
for use in the foregoing study. 

Tooke, "History of Prices," and 

Tooke and Newmarcb, " History of Prices from 1793 to 1856." 

G. Winter, "Zur Gescbicbte des Zinsfusses in Mittelalter," Zeit- 

schrift fiir Social und Wirlschaftsgeschichte, (Weimar), 1895,1V, 2. 

Arthur Crump, "English Manual of Banking," (4th ed., London, 

1879). PP- Mi-4- 

Gives Bank of England rates for 1694-1876. 



439] Appreciation and hiterest. 



97 



Alph. Courtois fils, " Histoire des Banques en France," (Paris, 1881). 
Gives rate of interest at the Bank of France, iSoo-1880. 

Wilhelm von Lucam, " Die Oesterreichische Nationalbank wahrend 
der Dauer des dritten Privilegiums," (Vienna, 1876), p. 121. 
Gives rates for Bank of Austria, 1817-75. 

"Jahrbiicher fiir Nationalokonomie und Statistik," February, 1896, 
pp. 282-83. 

Gives bank and market rates for London, Paris, Berlin, Amsterdam, 
Brussels, Vienna and St. Petersburg, 1841-80 by decades, and 1881-95 by 
years. 

" Handworterbuch der Staatswissenschaften," Article "Banken." 
Gives rates for Bank of Prussia and Germany, iS47-89i^^for Bank 
of Austria, 1878-89 ; Switzerland, 1883-88. <^^^ 

A. N. Kiaer, " Om seddelbanker, " (Kristiania, 1877). 

Contains diagram of bank rates at Kristiania, Stockholm and Kjoben- 
havn, 1853-76. 

M. G. Mullhall, "Dictionary of Statistics," (London, 1892), pp. 76, 
607. 

Gives rates for countries of Europe by five and ten year periods since 
1850. 

William Farr, "On the valuation of railroads, telegraphs," ^ic, Jour- 
nal of the Royal Statistical Society, September, 1S76, pp. 464-530, 

" Report of the New England Mutual Life Ins. Co.," Boston, 1890. 
Gives rates realized by twenty representative insurance companies for 
1869-88, and for Massachusetts savings banks for 1877-89, and bank divi- 
dends in Boston, New York and Philadelphia. The rates realized by the 
insurance companies for the twenty years, 1869-88, inclusive, were 6.0, 
5.9, 6.1, 6.2, 6.5, 6.2, 6.5, 6.1, 5.6, 5.1, 5.0, 4.8, 4.8, 5.1, 5.1, 4.7, 4.7, 4.9, 4.7, 4.6, 
respectively. These represent (if the -writer mistakes not) the average 
rates earned on the par value of investments of all ages, some old, some 
new, some terminable soon and others having many years to run. For 
this reason they are of little or no use for the foregoing study. 

Robert GifFen, "Essay in Finance," second series, (London, 1886), 

P- 37- 

Seasonal variations of interest in connection with bank reserves, etc. 

F. M. Taylor, ' ' Do we want an Elastic Currency ? ' ' Political Science 
Quarterly, March, 1896, pp. 133-157. 

Gives diagram showing the relation of surplus reserves and rates of 
discount ; also seasonal variation of rate of discount. 

R. H. Inglis Palgrave, "Analysis of the Transactions of the Bank of 
England," (London, 1874). 

Gives rates, 1844-72, and seasonal variation, 1844-56 and 1857-72. Shows 
dependence of rate on ratio of reserve to liabilities. 

R. H. Inglis Palgrave, "Bank-rate in England, France, and Germany, 
1844-78 ; with remarks on the causes which influence the rate of 
interest charged ; and an analysis of the accounts of the Bank of 
England," (London, 1880). 

R. H. Inglis Palgrave, (London) Bankers' Magazine, March, April, 
May, 1878. 

Number of changes in bank rates of England, France, and Germany. 



^8 American Economic Association. [446 

Theodor Hertzka, "Wahrung und Handel," (Vienna, 1S76). 

Gives the number of weeks each rate lasted for the Banks of England, 
France, Germany, and Austria during 1844-73. 

George Clare, "Money Market Primer," (London, 1S91). 

Diagrams for seasonal variations of interest, bank reserves, etc. 

Commercial and Financial Statistics of British India. Second issue, 
(Government Printing OfSce, Calcutta), 1894, pp. 354-64. 

Monthly Discount, Bank of Bengal, 1861-94, and average quotations of 
government securities held in I,ondon. 

Report of the Secretary of the Treasury, 1893, p. 401. 
Report of the Comptroller of Currency, 1894, p. 179. 
H. W. Farnam, "Some Effects of Falling Prices," Yale Review, Au- 
gust, 1895. 

The last three references contain statistics of rates of interest realized 
on some United States Government bonds. 

R. A. Bayley, "National Loans of the United States", (Government 
Printing Ofl&ce, Washington, 1882). 

Gives rates of interest and price of issue of all United States loans from 
July 4, 1776, to June 30, 1880. 

"Dictionaire des Finances," Article "Interet." 
Gives rates at vrhich France has borrowed. 

The following tables of index numbers are appended 
in order that the reader may verify the periods of rising 
and falling prices which have been discussed in Chapters 
X and for the reason that many of the tables, notably 
those for India, Japan and China, have not hitherto 
been accessible to most readers. 



INDSX NUMBERS IN SEIVEN COUNTRIES.i 



England. 



1824 
1825 
1826 
1827 
182S 
1829 
1830 
1831 
1832 
1833 
1834 
1835 
1836 
1837 
1838 

1839 
1840 
1841 
1842 
1843 
1844 
1845 
1846 
1847 
1848 
1849 
1850 
1851 
1852 
1853 
1854 
1855 
1856 
1857 
1858 

1859 
i860 
1861 
1852 
1863 
1864 
1865 
1866 
1867 
1868 
1869 
1870 
1871 
1872 
1873 
1874 
1875 
1876 
1877 
1878 
1879 
1880 
188 1 
1882 
1883 
1884 
1885 
1886 
1887 



1890 
1891 
1892 
1893 
1894 
1895 



105 
124 
108 
108 
97 
95 
97 
98 

93 
90 

93 
96 
103 

lOI 

loi 
no 
104 

102 
90 
85 
83 



94 
82 

77 
77 
79 
781 

95 
102 
loi 

lOI 

105 
91 
94 
99 
98 

lOI 

103 
105 

lOI 
102 
100 

99 
98 
96 
100 
109 
III 
102 
96 
95 
94 
87 



113 



134 
129 



Germany. 



100 
102 
114 
121 
124 
123 
130 
114 
116 
121 
118 
123 
125 
129 
123 
126 
124 
122 
123 
123 
127 
136 
138 
136 
130 
128 
128 
121 
117 
122 
121 
122 
122 
114 
109 
104 
102 
102 
106 
108 
109I 
106 
102 
92 
91 



United States. 



100 
118 
127 
129 
112 

115 
100 

95 
97 
94 
94 
105 
103 

94 
87 
85 
82 



79 



90 

84 
85 
88 
95 
95 
88 

83 
89 

99 
98 
105 
105 
109 
112 
114 

"3 

103 
100 

94 
104 
132 
172 
232 
188 
166 
174 
152 
144 
136 
132 
129 
130 
129 
123 
114 
105 
95 
105 
108 
109 
107 
103 
93 
93 
94 
96 
98 
94 
94 



83 



100 
100 
loi 
104 
119 

134 
149 

156 
164 
165 
167 
167 
166 
167 
166 
162 
158 
151 
144 
141 
139 
143 
151 
153 
159 
155 
156 
156 
157 
158 
163 
168 
169 



India. 



95 
99 
121 
125 
119 
112 
99 

96 
97 
95 
99 
loi 
104 
107 
103 
104 

"5 
119 



Japan. 



104 
104 
105 
102 

105 
114 

145 
160 

175 
159 
130 
116 
116 
107 
109 
112 
116 
124 
123 
124 
129 



China. 



100 
103 
III 
10 1 
106 
III 
105 
no 
108 
103 
104 
105 
107 
105 
100 
105 
104 
104 
108 
109 



1 For England, the figures for prices are from Jevons and Sauerbeck. Those 



lOO American Economic Associatio7i. [442 

from Sauerbeck begin in 1852. They are taken from the Aldrich report (I, 247) 
and from the Journal of the Royal Statistical Society, March, 1S96. Those from 
Jevons are from 1824 to 1852 inclusive, and are taken from his " Investigitions in 
Currency and Finance." In order to make ihe tables of Jevons and Sauerbeck 
continuous, Jevons' number for 1S52 is called 78 (i. e., Sauerbeck's for that year) 
instead of 65 as given in the "Investigations," and all the other numbers are 
raised in the ratio 78 : 65. Jevons' figures are for forty commodities ; Sauerbeck's 
for fortj'-five. The index numbers for English wages are from the article by 
Bowley in the Journal of the Royal Statistical Soceety, June, 1895. 

The German numbers are from Soetbeer, Heinz and Conrad. Those for 1851-gi 
inclusive, are from Soetbeer, continued by Heinz, and given in the Aldrich report 
(I, 294) ; those for 1891-95 inclusive, are from Conrad, as given in "his JahrbUcher^ 
1S94-6, but are all magnified in the ratio 109 : 98 in order to make the series con- 
tinuous, since Heinz's figure for 1891 is 109, and Conrad's 98. The statistics of 
Soetbeer and Heinz cover 114 commodities. 

The French numbers are from the Aldrich report (I, 335) founded on the figures 
of the Commission permanente des valeurs. They cover only sixteen articles. 

The figures for the United States are those of Professor Falkner in the Aldrich 
report (I, 9, 13), the weighted averages (last method) being employed. 

Those for India, Japan and China are from the Japanese Report of the Com- 
mission for investigation of monetary systems, 1S95. The writer is under great 
obligations to Mr. Ichi Hara, of Tokyo, for a copy of the report, and to Mr. 
Sakata of Yale University, for translating the tables. 

That for India is an average of three tables which cover respectively twentj'-one 
articles of export, sixteen articles of export priced at Calcutta and Bombay, and 
eight grains at Bombay. That for Japan is an average of three tables, of forty- 
two articles at Tokyo, sixteen at Osaka and thirty. one articles of export. That 
for China is an average of three tables, of twenty inland commodities, seventeen 
articles of export and fifteen food-stuffs in Shanghai. 

The tables for India were based on official statistics, those for Japan on in- 
formation from guilds and merchants, and those for China on the reports of the 
consuls of Japan and England (Mr. Jameson) in China. 

In the Japanese report the prices for Japan are reduced to a silver basis. As 
silver was at a premium up to 1S85 it has been necessary in constructing the 
above table to reconvert into currency by applj'ing the premium for 1873-85, viz.: 
4, 4i 3) I1 3) 10) 32, 48, 70, 57, 26, 9, 5 per cent, respectively. 



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Contents of No. XVI, December, 1895. 



Tendencies of Thought in Modern Judaism. 
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Octavius Brooks Frothingham. 

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Cardinal Manning, St. George Mivart. 
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